# Fast-Learning Grasping and Pre-Grasping
via Clutter Quantization and Q-map Masking

Dafa Ren1, Xiaoqiang Ren1, Xiaofan Wang1, S. Tejaswi Digumarti2 and Guodong
Shi2 $1$: School of Mechatronic Engineering and Automation, Shanghai
University, Shanghai, 200444, China. E-mails: (dafaren, xqren,
<EMAIL_ADDRESS>Sydney Institute for Robotics and Intelligent Systems,
The University of Sydney, Sydney, NSW 2006, Australia. E-mails:
(tejaswi.digumarti<EMAIL_ADDRESS>
###### Abstract

Grasping objects in cluttered scenarios is a challenging task in robotics.
Performing pre-grasp actions such as pushing and shifting to scatter objects
is a way to reduce clutter. Based on deep reinforcement learning, we propose a
Fast-Learning Grasping (FLG) framework, that can integrate pre-grasping
actions along with grasping to pick up objects from cluttered scenarios with
reduced real-world training time. We associate rewards for performing moving
actions with the change of environmental clutter and utilize a hybrid
triggering method, leading to data-efficient learning and synergy. Then we use
the output of an extended fully convolutional network as the value function of
each pixel point of the workspace and establish an accurate estimation of the
grasp probability for each action. We also introduce a mask function as prior
knowledge to enable the agents to focus on the accurate pose adjustment to
improve the effectiveness of collecting training data and, hence, to learn
efficiently. We carry out pre-training of the FLG over simulated environment,
and then the learnt model is transferred to the real world with minimal fine-
tuning for further learning during actions. Experimental results demonstrate a
94$\%$ grasp success rate and the ability to generalize to novel objects.
Compared to state-of-the-art approaches in the literature, the proposed FLG
framework can achieve similar or higher grasp success rate with lesser amount
of training in the real world. Supplementary video is available at
https://youtu.be/e04uDLsxfDg.

##  I INTRODUCTION

Grasping objects is one of the basic tasks of robotic manipulation. While it
may seem trivial for a human to pick an object from a pile, it is quite
challenging to train a robotic manipulator to do the same. One of the first
challenges is due to the presence of clutter in the environment. Partial
visibility of an object of interest and obstacles obstructing the manipulator,
in an object-rich environment, impede a successful grasp. Secondly, in a
typical industrial or logistics automation application, objects to be grasped
or avoided are constantly updated. This requires the development of algorithms
that can generalize well to previously unseen objects. Furthermore, collecting
data from real robots to train a grasping algorithm is expensive and time
consuming. Hence, an ideal robotic grasping solution should be able to tackle
these challenges.

Figure 1: Our robot is able to grasp objects in highly cluttered environments.
Our hardware setup consists of (1) a UR5e robot arm, (2) an Intel Realsense
RGB-D camera and (3) an RG2 gripper.

One way to address clutter in the environment is to perform a pre-grasping
actions, such as moving or shifting objects around, to facilitate grasping. In
recent years, such approaches are being actively studied [1, 2] and are
gaining popularity. However, the approaches developed so far either have a low
success rate or need a long training time in real world, which is not amenable
to the short deployment times desired by the industry.

In this paper, we propose a learning based framework (see Fig. 1) that enables
accurate grasping in cluttered environments with minimal real-world data. To
achieve this, we first define two pre-grasping manipulation primitives:
pushing and shifting. We use these primitives to increase the probability of
grasping. We then train an end-to-end self-supervised learning network without
human interaction based on model-free deep reinforcement learning in
simulation. This network, when transferred to real world, performs strongly
and generalizes well to novel objects. To be specific, the key aspects of our
system are:

  * •

We introduce clutter quantization maps to characterize environmental clutter.
Using these maps, we design a novel pre-grasping reward function that
associates rewards for moving actions with the change of environmental
clutter.

  * •

We propose a shifting action, in addition to pushing, which helps in dealing
with clutter better.

  * •

We introduce a mask function which promotes efficient learning by focusing on
meaningful and precise pose adjustment.

  * •

We extend the fully convolutional network (FCN) for reward estimation. The
network trained in the simulation environment is able to reach a success rate
of more than 90$\%$ only in 2.5 robot hours in the real-world training.

##  II RELATED WORK

Robotic manipulation, and in particular grasping, are active areas of research
within robotics. Classic analytical approaches [3] find stable force-closure
for known objects by utilizing 3D models of objects and their physical
properties. Recent years have witnessed a spurt of progress in deep learning
based computer vision and thus data-driven approaches to robotic manipulation
have become a research hotspot.

Data-driven approaches can be divided into two groups based on whether they
are model-based or not. Model-based data-driven approaches usually sample
grasps using the combination of object detection [4], pose estimation [5, 6,
7] and grasp estimation [8, 9] to pick the objects. But these approaches
usually leverage object specific knowledge (i.e., shape, pose). Consequently
their ability to generalize to unknown object classes and novel shapes is
limited. While real-world datasets with a large amount of labelled data, such
as [10, 11, 12], have been developed to overcome this issue, real-world data
collection and labelling is still time consuming, laborious and expensive.

In contrast, some data-driven approaches explore model-agnostic grasping
strategies that directly link visual data to candidate grasps [13, 14, 15].
Our approach is based on model-free deep reinforcement learning. Using
reinforcement learning enables us to learn more extensive grasp representation
through exploitation and exploration in a self-supervised way. Model-agnostic
learning also shows great results for generalizing to novel objects [2].

Handling clutter is another active area of research. To mitigate collisions
introduced by clutter, pre-grasping actions such as shifting and pushing, have
been proposed as manipulation primitives [16, 17, 18]. Kalashnikov et al. [19]
trained a QT-opt network for grasping, resulting in a grasping success rate of
96$\%$ for generalizing to unknown objects. In addition, the robots implicitly
learned other non-prehensile actions like pushing. However, their robot setup
relied upon over 580K real-world grasp attempts on 7 real robotic systems.
Berscheid et al. [2] used shifting actions to increase the grasping
probability and removed the need of shifting sparse rewards by making shifting
directly dependent on the change in the success rate of grasping. Their system
improved the grasp rate to 98.4$\%$, at the cost of around 25000 grasp and
2500 shift training data. Both of these methods consume a large number of
real-world training data. In this work, we train out network in a simulation
environment and then fine-tune the pretrained network in the real world.

More closely related to our work is that of Zeng et al. [1], which introduced
a $Q$-learning framework to learn the complementary pushing and grasping
strategies simultaneously. They utilized a Fully Convolutional Network (FCN)
as a function approximator to estimate the $Q$ function of the reinforcement
learning framework. This approach used significantly less training data than
[19], but the success rate was lower. Analogous to this method, our pre-
grasping actions include not only a pushing primitive, but also an additional
shifting primitive to further enlarge grasping task scenarios. We also extend
the FCN by utilizing a combination of skip connections [20] and upsampling to
improve learning efficiency. Our experiments demonstrate that our method is
capable of grasping objects more accurately.

##  III APPROACH

Figure 2: Manipulation primitives. When faced with a scene where the target
cannot be directly grasped, the robot can first scatter objects by pre-
grasping actions such as push and shift, and then grasp them.
\begin{overpic}[width=433.62pt]{overview.eps} \put(39.0,35.0){$\times$}
\end{overpic} Figure 3: Overview. The visual 3D data observed by a statically
mounted RGB-D camera is orthographically projected to construct heightmaps.
Then, the heightmaps are rotated by 16 orientations for angles
$\theta_{i}=\frac{2\pi i}{16}$ and then fed into the FCN. With the combination
of skip connection and upsampling, the FCN model outputs dense pixel-wise maps
of Q values. Each pixel of dense pixel-wise map predicted by FCN represents a
different location on which to execute the primitive in the corresponding
angle. Finally, our robot arm performs the primitive selected by mask
function.

We formulate the task of robotic grasping as a Markov decision process (MDP),
which is defined by its tuple $(\mathcal{S},\mathcal{A},r)$ with the state
space $\mathcal{S}$, the action space $\mathcal{A}$, and the reward function
$r$. We train the the robot using deep reinforcement learning (Q-learning),
whose goal is to find the solution to the MDP, which is a policy
$\pi:\mathcal{S}\rightarrow\mathcal{A}$ mapping the current state
$s_{t}\in\mathcal{S}$ to an action at $a_{t}\in\mathcal{A}$ that maximizes the
sum of expected rewards. Considering the huge action space and associated
sparse rewards, we limit our process to a discrete action space to improve
sample efficiency.

###  III-A Manipulation primitives

We parameterize the action space to a tuple $(x,y,z,\theta_{i},\phi_{j})$,
where $(x,y)$ is given by dense pixel-wise map of $Q$ values outputted by the
deep network, $z$ is the height of the predicted point, $\theta$ is the
rotation angle around the $z$-axis and $i$ corresponds to the index of the
rotation angle with a size of 16 in our system (i.e., $\theta_{i}=\frac{2\pi
i}{16}$). The last parameter $\phi$ corresponds to the top-down grasping
action ($\phi_{g}$) or the preset moving action ($\phi_{m}$). The moving
action can either be a shifting or a pushing action.

In the execution phase of the action, the end effector of the robotic
manipulator reaches the $(x,y)$ coordinate given in the prediction map with
$z$ height, at an angle $\theta_{i}$. When the controller selects $\phi_{g}$,
the end effector grasps from top to bottom; when the controller selects
$\phi_{m}$, the moving action is a shifting or pushing action which is
determined by the height of the predicted point, which indicates whether there
is a target there. If there is a target object at the predicted location, the
end effector will choose the shifting action, otherwise a pushing action is
taken to disperse the targets which cannot be grasped due to obstruction (see
Fig. 2).

###  III-B Rewards

We design reward functions for grasping and moving actions as follows. When
the end effector performs the grasping action and reaches the target position,
the end effector closes, and then the robot returns to a pre-specified _home_
position. If the antipodal distance between the fingers of the gripper is
greater than zero upon reaching the _home_ position, it is a successful grasp.
This corresponding reward $r_{g}$ for this grasping action is formulated as

$r_{g}(s)=\begin{cases}1,&\mbox{if successful grasping,}\\\
0,&\mbox{else.}\end{cases}$ (1)

The purpose of the moving action is to increase the probability of objects
that can be successfully grasped, in an environment with dense clutter or
ungraspable objects. This is done by scattering the objects. The moving reward
should therefore be related to the change in the environmental clutter. Notice
that a potentially good moving action will result in an increase of coverage
or a change of target position. For this reason, we parameterize the change of
environmental clutter by the change of the heightmap value $\mu(t)$ and the
change of coverage value $\eta(t)$. The heightmap change function $\mu(t)$ is
formulated as

$b_{i}(t)=\begin{cases}1,&\mbox{if $a_{i}(t+1)-a_{i}(t)>\delta$,}\\\
0,&\mbox{else.}\end{cases}$ (2) $\mu(t)=\sum_{i=1}^{N}b_{i}$ (3)

where $a_{i}(t)$ is the height above the work surface at pixel $i$ at time
$t$, $\delta$ is a preset threshold, and $N$ is the total number of pixels in
the heightmap (here, 224 $\times$ 224). The height $a_{i}(t)$ is computed by
projecting depth values, acquired from an overhead RGB-D camera,
orthographically onto the work surface, i.e. the table.

To define $\eta(t)$, we introduce _Clutter Quantization Map_ (see Fig. 4),
which is the heightmap after binarization and dilation. Specifically, each
pixel of heightmap is first set as 1 if the height value is larger than the
minimum height of the workspace and 0 otherwise. Then, a dilation is applied
to set to 1 the neighbours of each pixel that has a value of 1. The change in
coverage $\eta(t)$ is formulated as

$\eta(t)=\sum_{i=1}^{N}x_{i}(t+1)-\sum_{i=1}^{N}x_{i}(t)$ (4)

where $x_{i}(t)$ are the pixel value of the clutter quantization map at time
$t$, and $N$ is the number of pixels in the heightmap. Notice that the
dilation step fills gaps between adjacent objects and that objects that are
scattered have increased area as opposed to when they were clustered together.
Thus, this reward encourages scattering.

We now define a novel moving reward function as

$r_{m}(s)=\begin{cases}0.5,&\mbox{if $\mu>\tau_{1}$ or $\eta>\tau_{2}$,}\\\
0,&\mbox{else.}\end{cases}$ (5)

where both of $\tau_{1}$ and $\tau_{2}$ are preset thresholds.

Figure 4: Clutter quantization map. A potentially good moving action will
increase the number of pixels with a value of 1 (white pixels) in the clutter
quantization map (right) corresponding to the color image (left).

###  III-C Network

In designing the network architecture, we draw inspiration from the framework
proposed by Zeng et al. [1]. However, there are several key differences that
help our proposed framework outperform theirs.

We employ a dueling-DDQN [21] as the core of our framework. Unlike normal DDQN
[22], which can only update the value of one action per iteration, the value
stream $V$ of dueling-DDQN is updated with every update of the $Q$ values. In
addition, in our picking task, multiple actions corresponding to multiple
targets may share comparative rewards for a given state. Furthermore, the
robustness of the updates is also improved.

We use a Fully Convolutional Network (FCN) based on DenseNet-121 [23] to model
the $Q$ function of our dueling-DDQN (see Fig. 3). Each heightmap and
corresponding color image is rotated 16 times by an angle of $\pi/8$ radians,
which together form the state inputs. The network predicts dense pixel-wise
maps of $Q$ values of the same size as the output. Every pixel in the $Q$
value map represents a grasping or moving action primitive at the
corresponding 3D location. The rotation angle of the heightmap corresponds to
the rotation angle of the end effector. The dense pixel-wise parameterization
greatly simplifies the action space and speeds up the convergence speed.

The feature layer output of DenseNet-121 is bilinearly upsampled to 4 times
after 1 $\times$ 1 convolutional layer interleaved with ReLU and batch
normalization, followed by channel-wise concatenation with the corresponding
intermediate feature of DenseNet-121. The resulting concatenated feature then
passes through Conv, ReLU, Batch normalization layers and additional 4 times
bilinear upsampling to obtain a high-precision dual-channel dense pixel-wise
map, each of which corresponds to grasping map and moving one, respectively.

Unlike in [1], where two separate FCNs are trained for the grasp and push
actions, we train a single FCN which outputs a dual-channel pixel wise map for
each of the actions. In our experiments, our simple yet efficient network
structure takes only 0.7s to calculate the next action even if the size of
action space is $224\times 224\times 32$, which is much faster than Zeng et
al. [1] (i.e., 1.2s). In addition, the combination of skip connections [20]
and bilinear upsampling in our FCN further boosts accuracy.

###  III-D Exploration Policy

Since efficient exploration contributes to data-efficient learning, we
introduce two masks namely the grasping mask $\rho_{g}$ and the moving mask
$\rho_{m}$ and incorporate them into the exploration policy. The system makes
an action decision based on the prior probability maps

$\pi_{e}:\mathop{\arg\max}_{a}\rho\circ Q$ (6)

where $\circ$ is the Hadamard product, $\rho$ may be $\rho_{g}$ or $\rho_{m}$
according to the action taken, and $Q$ are the dense pixel-wise maps of $Q$
values. We filter the $Q$ maps by the masks, the effect of which is
illustrated in the bottom row of Fig. 5.

Grasping Mask $\rho_{g}$ is a binary mask, generated from the heightmap by
setting a pixel to 1 if the height value at that pixel is greater than the
minimum height of the workspace and 0 otherwise. Since the model parameters
are initialized randomly, in the early stages of training, the network will
most likely predict incorrect grasping positions and try to grasp in the
object-less background area. As a result, the training data essentially
consists of negative samples. The mask $\rho_{g}$ prevents the robot from
persisting exploration in these object-less areas and thereby encourages the
system to focus on the adjustment of accurate grasping pose in the desired
target areas (see Fig. 5).

Moving Mask $\rho_{m}$ is generated from $\rho_{g}$ by dilation, because the
areas of interest for a moving action are the target objects and their
surrounding areas. The training samples for moving actions occur relatively
less frequently than those of grasping actions as they appear only in
scenarios where a grasp is not possible. Hence, using this mask helps the
system to focus solely on the areas of interest and thus provide more
meaningful training data.

Figure 5: Mask function. The system performs the grasping or moving action in
the area (top row) with high success probability compulsively after using mask
function. The dense pixel-wise maps of $Q$ values are visualized as heat maps
(bottom row).

To improve the exploratory degree and sample diversity, our exploration policy
employs $\epsilon$-greedy strategy. Since the system iteration has one-step
lag and the last action may not change the state, the system may make the same
wrong decision as the previous step, which reduces the validity of data and
training speed. To cope with this, if the execution location of the current
step is the same as the previous step, the action in the previous step will
not be chosen at the current step. We will select one of the actions
corresponding to the $M$ maximum action-value function uniformly (here,
$M=10$). Through this strategy, our system avoids potential repeated failures.

##  IV EXPERIMENTAL RESULTS

The system uses an AMD 3970X processor and an NVIDIA RTX 2080Ti for computing.
Our system adopts prioritized experience replay [24], the loss function uses
the Huber loss function, and the optimizer is the Adam optimizer.

We design a series of experiments to evaluate the proposed approach, which we
call Fast-Learning Grasping (FLG). The goals of the experiments are 1) to
demonstrate that our approach can accurately grasp objects in different levels
of cluttered scenarios, 2) to show the significance of the novel network
structure and the exploration policy, 3) to test whether our algorithm is
capable of learning grasping effectively on a real system, and 4) to
investigate whether our model can directly generalize to novel objects.

###  IV-A Simulation Experiments

Our simulation environment consists of a UR5 robot arm with an RG2 gripper in
CoppeliaSim [1] (shown in Fig. 6). We compare performance of our policies
trained with different number of objects (see Fig. 7). When we train the model
in simulation with 10 objects, the system achieves a grasping success rate of
80$\%$ for 400 action attempts and a grasping success rate of 90$\%$ for 550
action attempts. In the same setting, the method of Zeng et al. [1] requires
more than a thousand training steps to achieve a success rate of about 80$\%$.
Our system outperforms their method with regard to training speed and success
rate. Although the training time is slightly extended in the more cluttered
environment, the final success rate is higher than 90$\%$. It can be seen in
Fig. 7 that our model can accurately grasp objects in different levels of
cluttered scenarios.

Figure 6: Simulation environment. Policies are trained in scenarios with
random arrangements of 20 objects. Figure 7: Comparison of performance of our
policies trained with different number of objects. The success rate of each
step is the average success rate of the first 200 steps of the current step.

We compare the controller’s pickup performance with the two baseline methods
to verify the impact of the exploration policy and network structure on the
training speed and grasping accuracy: 1) Dense Pixel-wise Estimation Network
(DPEN) is the same as our method in the network structure, but without our
masks. 2) $\rho$-FCN is an extension of VPG [1] by incorporating our masks.
The FCN of VPG directly takes the outputs of the feature layer of DenseNet-121
as the final $Q$ maps by sampling up 16 times without skip connections. We see
that our method outperforms both baseline methods with regards to training
speed and success rate (see Fig. 8). The poor performance of $\rho$-FCN is
likely due to the outputs of the network being bilinearly upsampled to 16
times. As a result, one prediction point corresponds to a patch area in
workspace. The final $Q$ maps are of low precision compared to ours. Moreover,
the results of our experiments show that the grasping success rates of the
models without the masks fluctuate by more than 15$\%$, and the training
process is relatively unstable. In particular, a relatively low success rate
is maintained for a long time in the early stages of training. In summary, we
infer that using masks in the model facilitates data-efficient learning while
using an extended FCN in the model improves the success rate.

Figure 8: Comparisons to Baselines. Taking the scenario of 13 targets as an
example, we compared the performance of our policy to the two baselines. Our
approach (FLG) achieves a higher and more robust grasping success rate in
shorter training time in comparison to baseline architectures.

Simulations are an attractive approach for training agents as they provide a
good starting point and alleviate certain safety concerns during the training
process for real-world applications [25]. We design a specific training
process to facilitate transferring of our model from simulation to the real
world. First of all, inspired by the idea of curriculum learning [26] and
domain randomization [27], we randomly place 10 blocks with different shapes
and colors into the workspace at the beginning of training. The system
basically does not need moving action in the case of fewer objects, thus, we
artificially reduce the number of moving actions at the first 500 steps. When
the iteration reaches 400 steps, we then increase gradually the number of
blocks until 20 are reached into the workspace. After 1500 steps, whenever the
robot empties the workspace, the environment is initialized into a preset
highly cluttered scene with a probability 0.2. From our observations, the
chances that the robot fails to grasp twice in a row are close to zero, under
normal conditions when the model learns to grasp accurately. If the robot
fails to grasp objects in two consecutive attempts, we consider the
environment to be highly cluttered and that a moving intervention is needed.
In this case, the system triggers a moving action to scatter the objects and
reduce clutter.

###  IV-B Real-World Experiments

In the real world, we also use a UR5e robot with an RG2 gripper as the end
effector. RGB-D images are captured from an Intel RealSense D415 mounted
rigidly above the workspace. During training, the robot automatically adds 20
objects into the workspace at random. Then, it grasps and places all of them
back until the workspace is empty and then restarts. In order to better
understand the ability of our model to meet the needs of different scenarios,
we train two models in the real world: 1) Grasping-only to learn high-
precision grasping strategy quickly, which makes the model focus on finely
adjusting grasping posture to grasp objects that are harder to grasp. Its
advantage is to empty the workspace quickly with high action efficiency. 2)
Grasping-Moving strategy is learning synergies between grasping and moving,
which is capable of emptying highly cluttered scenes with high grasping
success rate.

Figure 9: Grasping performance of our algorithm with and without pretraining
from the simulation environment in grasping-only mode.

First of all, in the grasping-only mode, we compare the performance difference
between the model directly trained only on real data and the model pretrained
in the simulation environment and fine-tuned with real-world data. The
training curve is shown in the Fig. 9. It can be seen that the pretrained
model has a higher performance in the early training stage, which achieves a
success rate of 90$\%$ with only 700 iterations. The pretrained model has
94$\%$ success rate after fine-tuning, while the one directly trained on real
data needs nearly 2500 steps to achieve 90$\%$ success rate. This experiment
shows that the pretrained model with fine-tuning is more effective than the
model directly trained from the real robot since the simulation data contains
significantly more diverse grasping samples.

TABLE I: Comparison of performance of state-of-the-art grasping algorithms based on Reinforcement Learning. Method | Grasp Success Rate | Iteration Steps
---|---|---
QT-opt [19] | 88$\%$ | 580000
VPG [1] | 68$\%$ | 2500
Berscheid et al. [2] | 98$\%$ | 27500
Song et al. [28] | 92$\%$ | 15000
Ours | 94$\%$ | 2500

The experimental data also shows that the sampling efficiency of our method is
extremely impressive. The superiority of our method is evident when we compare
the number of training steps required to achieve a similar success rate with
other state-of-the-art methods. Although the running environment is slightly
different, the results in Table I illustrate the learning efficiency of our
approach. While the other approaches require tens of thousands of steps when
fine-tuning their models to achieve a success rate of around 90$\%$, our
approach in comparison requires less than 1/10th of the number of training
iterations. Even the model directly trained from the real robot performs
better than the other approaches. The real robot also only needs 9s for each
motion. Furthermore, our method achieves a 90$\%$ success rate, at the cost of
training in the real world for only 2.5 hours. The number of picks and places
is about 350 per hour. It exceeds the number reported by Berscheid et al. [2],
which is 274 picks per hour.

Our algorithm requires the orthographic image of the depth image provided by
RGB-D camera as input, which poses a hidden challenge. Noise in the depth
images can lead to a in a decrease in the success rate of grasping, due to
incorrect heightmaps. Surprisingly, during our experiments, when the depth
image was corrupted by noise, the system would mistakenly grasp at noise
points in the early stages and then ignore the influence of the noise after a
few steps of training. This shows the robustness of our approach in making
action decisions.

Figure 10: Evaluating Grasping-only and Grasping-Moving in real-world tests with 20 objects randomly placed. TABLE II: Real-world results in the preset environment.  Method | Completion Rate | Grasp Success Rate
---|---|---
Grasping-only | 100$\%$ | 86$\%$
Grasping-Moving | 100$\%$ | 92$\%$

After that, we compare the performance of the combined grasping-moving
strategy versus the grasping-only strategy. This training curve is shown in
Fig. 10. As expected, the success rate of grasping in the early stages of
training for the grasping-only strategy is better than that of the grasping-
moving strategy because it focuses only on grasping. With the increase of the
number of training steps, the success rate of the two methods is similar, for
random initialization of the environment. Our observations show that in a
cluttered environment, grasping-only strategy learns how to fine-tune the
grasping position to pick up objects that are hard to grasp, while grasping-
moving method tends to move the position of objects and then grasp them.
However, as shown in the Table II, grasping-moving method shows a better grasp
success rate in the preset environment (examples of which are shown in the
Fig. 4). Notice that grasping-only method can reduce the environmental clutter
through failed grasp even if it cannot grasp directly, and then complete the
grasping task in a subsequent attempt.

Generalization is a key index for extending the range of applications in
industry and logistics automation. We evaluate the ability to generalize to
novel objects in a collection of real-world scenes with unseen shapes
(examples of which are shown in the Fig. 11). Although our training set only
has blocks with regular shape, it is capable of generalizing to the objects
with different shapes. As shown in the Table III, the system achieved an
average success rate of 96.6$\%$ for clutter free scenes, and 94.7$\%$ for
cluttered scenes. Surprisingly, the system performs well not only on objects
similar to the training set such as erasers and glue sticks, but also on
objects with extremely irregular shapes. This means that our model has learned
a more generalized probability mapping based on model-free reinforcement
learning instead of over-fitting to the shapes of the training set.

TABLE III: Grasp success rate of novel objects.  Object | Isolation | Clutter
---|---|---
Charger | 95$\%$ | 92$\%$
Stapler | 96$\%$ | 96$\%$
Eraser | 98$\%$ | 97$\%$
Pliers | 95$\%$ | 95$\%$
Glue stick | 97$\%$ | 93$\%$
Marker | 97$\%$ | 98$\%$
Brush | 96$\%$ | 93$\%$
Screwdriver | 95$\%$ | 93$\%$
Scotch tape | 99$\%$ | 97$\%$
Toy | 98$\%$ | 93$\%$
Figure 11: Example of unknown objects for testing our system’s ability to
generalize to novel objects.

##  V DISCUSSION AND OUTLOOK

We have presented a solution for fast learning of grasping and pre-grasping in
cluttered environments. We evaluated the performance of the system in both
simulation and real world. The model trained in simulation achieved a grasp
success rate of 94$\%$ when deployed in real-world cluttered scenarios with
minimal real-world data. Since our solution is based on deep reinforcement
learning of visual input to learn grasping strategies without object models,
it can be extended to a variety of novel objects. The experimental results
show that our novel design improves both grasping performance and learning
efficiency. As we rely on simulation based learning, we eliminate the need for
large amounts of manual data collection and require no human participation in
the whole process. Moreover, it takes only 2.5 hours to fine-tune in the real
world to achieve a considerably high success rate, which makes our approach
feasible for practical deployment.

We also note the following limitations of our approach. Unlike Song et al.
[28], we restrict our action space representation to 4DoF in a discrete space
instead of 6DoF in a continuous space. As a result, we limit variety in
grasping poses and ignore path planning to reach the grasp point. On a
positive note, this facilitates efficient learning. Another limitation is that
the robot will persistently complete a grasping action when the controller
makes a prediction, even if the environment changes during the execution
process. This is likely to lead to failure in some cases, which is also the
main factor limiting the success rate of our grasping. We plan to address this
in future work by incorporating real-time decision making into the framework.

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decays of W and Z bosons, which have always been extremely hard to detect
using inclusive dijet samples, emerge very clearly from the QCD background.
The analysis can be extended to the case in which the resonance recoils
against a photon [111], or decays into a pair of b quarks [112].

To reiterate the previous message: high energy is a blessing even when we are
interested in searching low-mass objects, well below the kinematic reach,
since it provides a multitude of handles required to promote otherwise elusive
signatures into detectable final states!

###  8.5 Dark matter searches

The search for DM particles is another top-priority target of any future
collider. Of the motivations, possible explanations, and search strategies for
DM, you already learned a lot from other lectures at this school [113, 114],
so I give all of this for granted.

I start with one general comment, to put in perspective the value of DM
searches at a future collider. For all we know, DM could be anything from an
ultralight particle [115] in the ${\cal O}(10^{-20})$ eV mass range, with a
Compton wavelength as large as a galaxy, to a primordial black hole [116],
with a mass of several solar masses. There are models for almost every mass
window in between, from axions [117] to sterile neutrinos [118], from dark
photons to weakly interacting massive particles (WIMPs [19]). It is clear that
there is no single experiment, whether in space or in the laboratory, that can
guarantee the discovery of DM. Hopefully, at least one of those under way or
under planning will soon succeed. Its success will reward those who built it,
and those who proposed the relevant model. But this discovery will not
diminuish the value of all the other attempts, theoretical and experimental,
that have gone and will go into the search across the board. As a community,
we must endeavour to explore all reasonable hypothesis.

In this context, colliders provide a powerful window on the broad, and
theoretically well justified, class of WIMP models.

If at any point in the history of the early universe the DM is in thermal
equilibrium with the SM particles, then its relic density today can be
estimated by studying how it decouples from the SM, a process known as freeze-
out. For particles which are held in equilibrium by pair creation and
annihilation processes, $(\chi\chi\leftrightarrow{\rm SM})$ one finds the
simple relation that [119]

$\Omega_{\rm DM}h^{2}\sim\frac{10^{9}{\mathrm{G}eV}^{-1}}{M_{\rm
pl}}\frac{1}{\langle\sigma v\rangle}\,,$ (14)

where $\langle\sigma v\rangle$ is the velocity averaged annihilation cross
section of the DM candidate $\chi$ into SM particles, $\Omega_{\rm
DM}h^{2}\approx 0.12$ is the observed relic abundance of DM [28], $M_{\rm pl}$
is the Planck scale and order one factors have been neglected.

For a particle annihilating through processes which do not involve any larger
mass scales, the annihilation cross section scales as $\langle\sigma
v\rangle\sim g_{\rm eff}^{4}/M_{\rm DM}^{2}$, where $g_{\rm eff}$ is the
effective coupling strength which parameterises the process. It follows that

$\Omega_{\rm DM}h^{2}\sim 0.12\times\left(\frac{M_{\rm
DM}}{2\;\mathrm{TeV}}\right)^{2}\left(\frac{0.3}{g_{\rm eff}}\right)^{4}.$
(15)

This approximate relation implies that a DM candidate with a mass at or below
the TeV scale and which couples to the SM with a strength similar to the weak
interactions naturally has a relic density in agreement with observations.
Furthermore, as the DM mass is reduced, ever weaker couplings are required. On
one hand this is the main reason why it is hoped to find evidence for DM at
the LHC, but on the other hand it already shows that a higher energy collider
will be necessary to fully probe the WIMP paradigm for DM.

Eq. 15 shows that as the mass of DM increases, in order to maintain the
observed relic abundance, the annihilation cross section also has to increase.
This becomes inconsistent with unitarity of the annihilation amplitudes at
$M_{\rm DM}\lesssim 110$ TeV, the so called unitarity bound on the mass of DM
[120, 121]. Most well motivated models of WIMP DM do not saturate this bound,
but rather have upper limits on the DM mass in the TeV range.

For example, DM particles coupled to the SM via EW interactions, are subject
to mass upper limits of about 1 TeV (in the case of EW doublets, such as
supersymmetry higgsinos), and about 3 TeV (in the case of EW triplets, such as
the supersymmetric partners of the W/Z bosons). These mass values are well
beyond the reach of the HL-LHC, because of the low production rates. The
challenge to find them, or rule them out, is therefore left to a future high-
energy collider. At these high masses, EW symmetry leads to a further
difficulty: particles in EW multiplets tend to be degenerate in mass, with
electromagnetic mass splittings in the range of few hundred MeV, and decay
lifetimes in the range of several cm. The standard production/decay
signatures, such as $\rm pp\to$χ+χ${}^{-}\to$χ0χ0+leptons or jets, lead to
very little visible energy, and are not even recorded by the triggers. In
these cases, a crucial viable signature is the so-called “disappearing track”
[122]: the charged state travels for few cm through the tracking layers of the
detector, and suddenly disappears, vanishing into the non-interacting DM
particle and a small-momentum charged track, typically undetected. The trigger
is provided by a recoiling jet. Gaining sensitivity to these disappearing
tracks is a crucial criterion in the design of future trackers for the FCC-hh
experiments [11]. Without entering into the details of the analyses [123], we
report here the results in Fig. 33, which confirm that the reach for
discovery, or exclusion, of WIMPs at the upper mass end is achieved.

Figure 33: Expected discovery significance at 30 ab-1 with 500 pile-up
collisions. The black (red) band shows the significance using two alternative
tracker layouts, described in Ref. [123]. The band width represents the
difference between two models of the soft QCD processes.

For DM masses at the lower end of the WIMP spectrum, one typically expects
that annihilation proceeds through a mediator with $M_{\rm med}>2M_{\rm DM}$.
Then the annihilation cross section is suppressed by $(M_{\rm DM}^{4}/M_{\rm
med}^{4})$. Assuming that no mediator particle exists with a mass below the
Higgs mass, then this puts a lower bound close to a GeV on the mass of the
WIMP DM candidate. In this region, and in general in the mass region which
allows for direct DM decays of the Higgs or Z bosons, the sensitivity to their
invisible decays discussed in Section 4 and 5 provides an extensive probe to
probe dark sectors of relevance to the DM issue [9].

While there is no firm no-lose theorem yet, covering all potential loopholes,
the multiple studies carried out so far provide solid evidence that the
combination of FCC-ee and FCC-hh could indeed exhaustively close the WIMP DM
window.

###  8.6 Other discovery opportunities

As mentioned at the beginning of this section, there are countless areas of
opportunity for direct discovery, throughout the mass and coupling spectrum. I
briefly show here a few additional examples, which emphasize once again the
great potential coming not only from the high-energy reach of the pp collider,
but also from the increased sensitivity in the low-mass region, thanks to the
high statistics and the flexibility of the overall program.

To complete the exploration of the Higgs properties, it is important to
guarantee sensitivity to exotic decays, which could arise in a variety of BSM
models [124], particularly in the context of Higgs-portal scenarios, where the
Higgs boson is the only SM particle coupled to an otherwise dark sector via
dim-4 interactions like $|H|^{2}\varphi^{2}$. Figure 34 shows the prospects
for the detection of decays covering a wide array of possible final states.
The sensitivity of the $\rm e^{+}e^{-}$ collider is crucial, as shown by the
significant improvement over the HL-LHC prospects, in spite of the much higher
Higgs statistics available. It is possible that the FCC-hh could also
contribute to this searches, at least in some channels, although dedicated
studies have not been carried out as yet.

Figure 34: Sensitivity to exotic Higgs decays at FCC-ee. From [10, 125, 126].

A notable feature of the Higgs portal interaction $|H|^{2}\varphi^{2}$ is that
it respects a $\mathcal{Z}_{2}$ symmetry, $\varphi\to-\varphi$. Such a
symmetry can make $\varphi$ stable or, if it is explicitly broken by some
small amount, $\varphi$ may be long-lived. This alone motivates searching for
exotic decays of the Higgs boson to particles that decay on a macroscopic time
scale. Such scenarios arise frequently in theories beyond the SM, such as
models of neutral naturalness. Projections for sensitivity to such exotic
Higgs decays are shown in Fig.35 for a variety of collider scenarios,
including the HL-LHC, FCC-hh, LHeC and FCC-eh. At hadron colliders two
different triggering strategies are considered. One involves VBF-tagging and
displaced vertices and the other only a single lepton and displaced vertices.
It is notable that at FCC-hh one can access exotic Higgs decays down to
branching ratios smaller than $10^{-6}$, demonstrating extreme sensitivity to
very exotic Higgs decays. Furthermore, due to the cleaner detection
environment, the FCC-eh projections can push to shorter lifetimes than are
accessible at FCC-hh.

Figure 35:  Projected exclusion limits on exotic Higgs decay branching
fractions to LLPs $X$ as a function of lifetime $c\tau$ for the LHeC, and for
the FCC-eh at two different energies of the electron beam, 60 and 240 GeV. The
excluded branching ratio scales linearly with luminosity under the assumption
of no background. The LLP mass in the plot is 20 GeV. For comparison, an
estimate for the sensitivity of proton colliders without background is shown
(blue), as well as a very optimistic estimate which assumes extremely short-
lived LLP reconstruction (orange), from [127]. This plot is taken from [128].

A similar approach can be applied to Z decays. In this case, there is no way
any alternative collider could match the power of the $10^{13}$ Z statistics
of FCC-ee!

Figure 36:  The 95% C.L. sensitivity reach for various exotic Z decay
branching ratios at the future Z-factory, where the Tera Z benchmark
corresponds to the FCC-ee Z-pole run. This figure is taken from [126], where
further details on the various decay topologies considered, including any
model-dependence, are presented.

##  9 Final remarks

The physics program of the FCC facility goes well beyond what we have shown
here. We focused in these lectures on the most visible elements, which support
the promise to fulfill an ambitious program of measurements related to the EW
symmetry breaking sector of the SM, and of searches for new physics. Much more
is discussed in the literature, and in the more complete physics reports and
CDRs. There it is shown that the FCC can extend our knowledge over many fronts
I did not cover. The mass and EW couplings of the top quark will be studied
with great precision at FCC-ee, and the huge statistics of FCC-hh will push
the search for rare or forbidden decays, and the sensitivity to anomalous
couplings, beyond what can be achieved elsewhere. Should neutrino masses and
mixings have their origin at the EW scale, the combination of several
observables at FCC will be able to probe the underlying physics. Flavour
phenomena, in the b and in the $\rm\tau$ sectors, will be explored with a
sensitivity often exceeding what will be known by the end of the HL-LHC and of
the Belle II programs, thanks to the statistics and clean experimental
environment of Z decays at FCC-ee. The study of QCD dynamics will attain new
levels of precision, in the determination of $\alpha_{s}$, of the proton PDFs,
in the modeling of the structure of jets, and more. The program of collisions
with and between heavy ions will open new avenues in the exploration of the
high-density phase of QCD, for example acquiring new hard probes (notably the
top quark and its decay products) to monitor the thermalization phase of the
quark-gluon plasma, and extending to much higher multiplicities the studies of
collective effects.

When looking at the whole program, one feature emerges very clearly: the
overall coherence, completeness and far-sightedness. Each component of the
programme is part of a big picture, and contributes in different ways to the
overall complementarity and synergy. No stone will be left unturned, not a
byte of data will be redundant. The huge statistics at the Z is not just a
blessing for EW precision physics, but provides also opportunities for
discovery in otherwise elusive areas, from exotic Higgs decays, to flavour
physics of the tau lepton and b quark, to neutrino physics. The run at the top
threshold, primarily focused on the study of the top mass and couplings, will
also push the precision of Higgs measurements, thanks to the emergence of the
WW$\to$H fusion channel, and thanks to the indirect access to the ttH and HHH
couplings. The FCC-ee results (e.g. the total H width and the absolute
H$\to$4$\ell$ branching ratio, or the vector/axial EW top couplings) will
provide the inputs necessary to fully exploit the potential precision of
systematics-dominated FCC-hh measurements, such as the branching ratios for
rare decay modes or the Higgs self-coupling. FCC-eh will complement the set of
inputs, providing the most accurate determination of the proton PDFs; but it
will also add to the ee and hh results with its own Higgs studies,
particularly sensitive to the HWW and Hbb couplings, and with a complementary
sensitivity to new physics phenomena, from neutrino observables, to long-lived
particles or leptoquarks. The FCC-hh, finally, will add its own critical
contributions to the precision measurements in the Higgs and EW symmetry
breaking sectors, and will push to the highest masses the direct search for
new particles, with a reach that promises to confirm or exclude in a
conclusive way the existence of WIMP DM candidates or the strong 1st order
nature of the EW phase transition.

All of these elements make the FCC the most comprehensive facility to extend
the exploration of high-energy physics throughout the XXI century.

Acknowledgements: I am grateful to Tilman and Tracy for the kind inivitation
to lecture at TASI, and to the whole school team for their support and
assistance. The students were fantastic, it’s been a real pleasure and honour
to spend time with them! The material for these lectures is the result of
several years of work by countless colleagues, at the LHC, FCC, CEPC, CLIC and
ILC: a world-wide community sharing a challenging vision for the future of our
field, extending well through the XXI century. My thanks go therefore to all
my friends, who are working hard to turn this vision into a reality!

##  Appendix A Simple features of the energy scaling of hard cross sections in
hadronic collisions

As well known, and recalled in the lectures by Frank Krauss, the differential
cross section for a process in hadronic collisions is represented as follows:

$d\sigma\;=\;\int\;\sum_{i,j}\;dx_{1}dx_{2}\,f_{i}(x_{1},Q)f_{j}(x_{2},Q)\
d\hat{\sigma}_{ij}$ (16)

where $Q$ is the factorization scale, namely the characteristic hard scale of
the partonic process, $x_{1,2}$ are the momentum fractions of the protons
carried by the initial state partons, $f_{i}(x)$ are the parton distribution
functions (PDFs) for the parton of flavor $i$, and the partonic cross section
is given, in terms of the squared and averaged matrix element, by:

$d\hat{\sigma}\;=\;\frac{1}{2\hat{s}}\int\prod_{i}\frac{d^{3}p_{i}}{(2\pi)^{3}2p_{i}^{0}}\;(2\pi)^{4}\,\delta(P_{in}-P_{out})\times\overline{|M|^{2}}$
(17)

It is an easy exercise to reexpress the integration measure $dx_{1}\,dx_{2}$
as $dy\,d\tau$, where ($S=4E_{beam}^{2}$):

$\tau=x_{1}x_{2}=\frac{\hat{s}}{S}\quad,\quad
y=\frac{1}{2}\log\frac{E^{in}+P_{z}^{in}}{E^{in}-P_{z}^{in}}=\frac{1}{2}\log\frac{x_{1}}{x_{2}}\quad\Rightarrow
x_{1,2}=\sqrt{\tau}e^{\pm y}\;.$ (18)

The result can then be written as:

$d\sigma=\int\frac{d\tau}{\tau}\ \,\times\,\tau\frac{d{\cal
L}}{d\tau}\,\times\,d\hat{\sigma}$ (19)

with

$\frac{d{\cal
L}}{d\tau}\;=\;\int_{y_{min}}^{y_{max}}\,dy\,f(\sqrt{\tau}e^{y})f(\sqrt{\tau}e^{-y})\;=\;\int_{\tau}^{1}\;\frac{dx}{x}f(x)f(\tau/x)\quad(y_{min,max}=\pm
0.5\log\tau)\;.$ (20)

Notice that, for fixed partonic center-of-mass energy $\sqrt{\hat{s}}$, the
dependence of the cross sections on the beam energy $E_{beam}$ is all built
into the partonic luminosity factor $\tau d{\cal L}/d\tau$, since both
$\hat{\sigma}$ and $d\tau/\tau$ are independent of $E_{beam}$ 666Notice
however that kinematic cuts to the final state particles will affect the
integration ranges in an energy-dependent way..

Several useful results, which help getting a feeling for how cross sections
behave at high energies, can be easily obtained with simple assumptions and
parameterizations of the PDFs. Consider for example a $2\to 1$ process such as
the production of a H boson in the $gg$ channel. In this case it is easy to
show that, for a final state of mass $m$ ($\tau=m^{2}/S$):

$\frac{d\sigma}{dy}=\frac{\pi}{m^{4}}\overline{|M|^{2}}\;\tau\,f(\sqrt{\tau}e^{y})f(\sqrt{\tau}e^{-y})$
(21)

If we parameterize $f(x)\sim 1/x^{1+\Delta}$, which as we shall see later is a
good approximation over a broad range of $x$ values, we can obtain

$\displaystyle\frac{d\sigma}{dy}$ $\displaystyle=$
$\displaystyle\frac{\pi}{m^{4}}\overline{|M|^{2}}\;\frac{1}{\tau^{\Delta}}$
(22) $\displaystyle\sigma$ $\displaystyle=$
$\displaystyle\frac{\pi}{m^{4}}\overline{|M|^{2}}\;\frac{1}{\tau^{\Delta}}\;\log\frac{1}{\tau}$
(23)

The first equation says that the rapidity distribution $d\sigma/dy$ is flat in
$y$, in the $y$ range up to the kinematic limit, $|y|=\log(E_{beam}/m)$. The
total cross section will grow with energy at least logarithmically, to reflect
the increased rapidity range. The growth is faster if $\Delta>0$ 777Notice
that $\Delta$ must be smaller than 1, to ensure that the total momentum
fraction carried by a parton $i$, $\int_{0}^{1}dx\,xf_{i}(x)$, be finite..

As a first simple application of these relations, let us estimate the Higgs
cross section growth between LHC ($\sqrt{S}=14$ TeV) and FCC-hh
($\sqrt{S}=100$ TeV). Equation 23, with $m_{H}=125$ GeV, gives:

$\frac{\sigma_{100}(gg\to H)}{\sigma_{14}(gg\to
H)}\sim\left(\frac{100}{14}\right)^{2\Delta}\times\;\frac{\log(100\,\mathrm{TeV}/m_{H})}{\log(14\,\mathrm{TeV}/m_{H})}\sim
15\;,$ (24)

where we used $\Delta\sim 0.6$, as suggested by the approximate fits in Fig.
37. The actual result, as shown in Table 3, is 18, so not bad for a simple-
minded approach. In the case of W production, replacing $m_{H}$ with
$m_{W}\sim 80$ GeV, and for $\Delta\sim 0.4$ (see Fig. 37), gives a W cross
section increase of about 7, compared to the factor of 6.5 increase of an
actual complete calculation (1.3 vs 0.2 $\rm\mu b$).

Exercise: Eqs. 22 and 23 assume $\Delta$ is the same for both incoming
partons. This is not a bad assumption for $u$ and $\bar{u}$, as shown in Fig.
37, but would not hold for a $qg$ initial state. Discuss.

Figure 37: Testing the simple approximations
$f(x)\sim(1-x)^{\beta}/x^{\alpha}$ for the gluon, up and antiup quarks, at
different values of the factorization scale $Q$.

Figure 38: Rapidity spectra of systems of mass $M_{X}$, produced in 100 TeV pp
collisions by various initial-state channels.

In reality, the behaviour of the rapidity distribution at $y\sim y_{min,max}$
is not a sharp edge, since when $|y|\to y_{max}$ then $x\to 1$ for one of the
two initial partons, and the parameterization $f(x)\sim 1/x^{1+\Delta}$ is
clearly inappropriate. To be more realistic, we can replace this by

$f(x)\sim\frac{(1-x)^{\beta}}{x^{1+\Delta}}\;.$ (25)

Figure 37 compares this approximation against the actual PDF for the gluon,
the u quark and the $\rm\bar{u}$ antiquark, for various values of the
factorization scale $Q$. While the approximtion is not perfect, it is
remarkable that it does such a good job, over a range of $x$ from $10^{-5}$
and $\sim 0.2-0.3$. Given the $1/x^{1+\Delta}$ behaviour, these PDFs vary by 6
or 7 orders of magnitude in this $x$ range, and, by choosing suitable
parameters $\Delta$ and $\beta$, the approximate functional form maps out the
PDF behaviour within a factor better than 2! Notice also the peak structure of
the $u(x)$ distribution at $x\sim 0.2$, due to the valence contribution, which
cannot be properly modeled by the simple parameterization in Eq. 25. The
rapidity spectra of systems of different mass produced with different initial
states are shown in Fig. 38. Notice that the $\rm q\bar{q}$ and qg
distributions are broader than the gg one, since the valence quark
distribution is much bigger than the gluon at large $x$.

##  Appendix B FCC parameters

For reference, we summarize in this Section the key parameters established for
the design of the various components of the FCC facility. More details can be
found in Refs. [10, 11, 12].

###  B.1 FCC-ee

The main design principles of FCC-ee are as follows.

  * •

It is a double ring collider with electrons and positrons circulating in
separate vacuum chambers. This allows a large and variable number of bunches
to be stored. The beam intensity can thus be increased in inverse proportion
to the synchrotron radiation (SR) per particle per turn, to keep the total
power constant to a set value of 100 MW for both beams, at all energies.

  * •

A common low emittance lattice for all energies, except for a small
rearrangement in the RF section for the $\rm t\overline{t}$ mode. The optics
are optimised at each energy by changing the strengths of the magnets.

  * •

The length of the free area around the IP ($L^{*}$) and the strength of the
detector solenoid are kept constant at 2.2 m and 2 T, respectively, for all
energies.

  * •

A top-up injection scheme maintains the stored beam current and the luminosity
at the highest level throughout the experimental run. This is achieved with a
booster synchrotron situated in the collider tunnel itself.

As a requirement, the luminosity figures are very high, ranging from $2\times
10^{36}$cm-2s-1 per IP at the Z pole, and decreasing with the fourth power of
the energy to $1.5\times 10^{34}$cm-2s-1 per IP at the top energies. The run
plan spanning 15 years including commissioning is shown in Table 10. The
number of Z bosons planned to be produced by FCC-ee (up to $5\times 10^{12}$),
for example, is more than five orders of magnitude larger than the number of Z
bosons collected at LEP ($2\times 10^{7}$).

Table 10: Run plan for FCC-ee in its baseline configuration with two experiments. The number of WW events is given for the entirety of the FCC-ee running at and above the WW threshold.  Phase | Run duration | Centre-of-mass | Integrated | Event
---|---|---|---|---
| (years) | Energies (GeV) | Luminosity (ab-1) | Statistics
FCC-ee-Z | 4 | 88-95 | 150 |  $3\times 10^{12}$ visible Z decays
FCC-ee-W | 2 | 158-162 | 12 | 108 WW events
FCC-ee-H | 3 | 240 | 5 | 106 ZH events
FCC-ee-tt(1) | 1 | 340-350 | 0.2 |  ${\rm t\bar{t}}$ threshold scan
FCC-ee-tt(2) | 4 | 365 | 1.5 | 106 $\rm t\overline{t}$ events
Table 11: Reference parameters for operations at (HL-)LHC, HE-LHC and FCC-hh. More details on the structure of the minimum bias events at 100 TeV can be found in [129].  Parameter | Unit | LHC | HL-LHC | HE-LHC | FCC-hh
---|---|---|---|---|---
$E_{cm}$ | TeV | 14 | 14 | 27 | 100
Circumference | km | 26.7 | 26.7 | 26.7 | 97.8
Peak ${\cal L}$, nominal (ultimate) |  $10^{34}$cm-2s-1 | 1 (2) | 5 (7.5) | 16 | 30
Goal $\int{\cal L}$ | ab-1 | 0.3 | 3 | 10 | 30
Bunch spacing | ns | 25 | 25 | 25 | 25
Number of bunches |  | 2808 | 2760 | 2808 | 10600
RMS luminous region $\sigma_{z}$ | mm | 45 | 57 | 57 | 49
$\sigma_{inel}$ [129] | mb | 80 | 80 | 86 | 103
$\sigma_{tot}$ [129] | mb | 108 | 108 | 120 | 150
Peak pp collision rate | GHz | 0.8 | 4 | 14 | 31
$dN_{ch}/d\eta|_{\eta=0}$[129] |  | 6.0 | 6.0 | 7.2 | 10.2
Charged tracks per collision $N_{ch}$ [129] |  | 70 | 70 | 85 | 122
Rate of charged tracks | GHz | 59 | 297 | 1234 | 3942
$\langle p_{T}\rangle$ [129] | GeV/c | 0.56 | 0.56 | 0.6 | 0.7
$dE/d\eta|_{\eta=5}$ [129] | GeV | 316 | 316 | 427 | 765
$dP/d\eta|_{\eta=5}$ | kW | 0.04 | 0.2 | 1.0 | 4.0

###  B.2 FCC-hh and HE-LHC

The FCC-hh collider design, performance and operating conditions are discussed
in detail in Volume 3, Chapter 2, and summarized in Table 11. The key
parameters are the total centre-of-mass energy, 100 TeV, and the peak initial
(nominal) luminosity of ${5(25)}\times 10^{34}~{}$cm-2s-1, with 25 ns bunch
spacing. At nominal luminosity, the pile-up reaches 850 interactions per bunch
crossing. The feasibility and performance of alternative bunch spacings of
12.5 and 5 ns are under study (see Volume 2, Section 2.2.5). With two high-
luminosity interaction points, and taking into account the luminosity
evolution during a fill and the turn-around time, the optimum integrated
luminosity per day is estimated to be 2.3 (8.2) fb-1. The total integrated
luminosity at the end of the programme will obviously depend on its duration.
Assuming a 25 year life cycle, with 10+15 years at initial/nominal parameters,
allows a goal of 5+15=20 ab-1to be set. This has been shown to be adequate for
the foreseeable scenarios [130]. A luminosity range up to 30 ab-1is considered
for most of the physics studies. This allows the ultimate physics potential to
be assessed, considering that the two experiments will probably combine their
final results for the most sensitive measurements.

The current design allows for two further interaction points (IPs), where the
pp luminosity can reach ${2}\times 10^{34}~{}$cm-2s-1, with a free distance
between IP and the focusing triplets of 25 m. Apart from the case of heavy ion
collisions, no discussion of possible FCC-hh experiments using these lower-
luminosity IPs will be presented.

For the HE-LHC the asumptions are for a collision energy $\sqrt{S}=27$ TeV and
a total integrated luminosity of 15 ab-1, to be collected during 20 years of
operation.

Table 12: Beam and machine parameters. | Unit | Baseline | Ultimate
---|---|---|---
Operation mode | - | PbPb | pPb | PbPb | pPb
Number of Pb bunches | - | 2760 | 5400
Bunch spacing | [ns] | 100 | 50
Peak luminosity (1 experiment) | [$10^{27}~{}$cm-2s-1] | 80 | 13300 | 320 | 55500
Integrated luminosity (1 experiment, 30 days) | [nb-1] | 35 | 8000 | 110 | 29000

###  B.3 FCC-hh: Operations with Heavy Ions

It has been shown that the FCC-hh could operate very efficiently as a nucleus-
nucleus or proton-nucleus collider, analogously to the LHC. Previous studies
[131, 132] have revealed that it enters a new, highly-efficient operating
regime, in which a large fraction of the injected intensity can be converted
to useful integrated luminosity. Table 12 summarises the key parameters for
PbPb and pPb operation. Two beam parameter cases were considered, baseline and
ultimate, which differ in the $\beta$-function at the interaction point, the
optical function $\beta^{*}$ at the interaction point, and the assumed bunch
spacing, defining the maximum number of circulating bunches. The luminosity is
shown for one experiment but the case of two experiments was also studied:
this decreases the integrated luminosity per experiment by 40%, but increases
the total by 20%. The performance projections assume the LHC to be the final
injector synchrotron before the FCC [133]. A performance efficiency factor was
taken into account to include set-up time, early beam aborts and other
deviations from the idealised running on top of the theoretical calculations.
Further details on the performance of the heavy-ion operation in FCC-hh can be
found in Section 2.6 of the FCC-hh CDR Volume.

###  B.4 FCC-eh

The FCC-eh is designed to run concurrently with the FCC-hh. The electron-
hadron interaction has a negligible effect on the multi TeV energy hadron
beams, protons or ions. The electron beam is provided by an energy recovery
linac (ERL) of $E_{e}=60$ GeV energy which emerges from a 3-turn racetrack
arrangement of two linacs, located opposite to each other. This ERL has been
designed and studied in quite some detail with the LHeC design. For FCC-eh,
for geological reasons, the ERL would be positioned at the inside of the FCC
tunnel and tangential to the hadron beam at point L. There will be one
detector only, but forming two data taking collaborations may be considered,
for example, to achieve cross check opportunities for this precision
measurement and exploratory programme.

The choice of $E_{e}=60$ GeV is currently dictated by limiting cost. Desirably
one would increase it, to reduce the beam energy uncertainty and access
extended kinematics, but that would increase the cost and effort in a non-
linear way. This could happen, nevertheless, if one expected, for example,
leptoquarks with a mass of $4$ TeV which the FCC-eh would miss with a $60$ GeV
beam. Currently, the energy chosen, taken from the LHeC design, is ample and
adequate for a huge, novel programme in deep inelastic physics as has been
sketched above.

In concurrent operation, the FCC-eh would operate for 25 years, with the FCC-
hh. This provides an integrated luminosity of $\cal{O}$(2) ab-1, at a nominal
peak luminosity above $10^{34}$ cm-2 s-1, at which the whole result of HERA’s
15 year programme could be reproduced in about a day or two, with kinematic
boundaries extended by a factor of 100. The pile-up at FCC-eh is estimated to
be just 1. The forward detector has to cope with multi-TeV electron and hadron
final state energies, while the backward detector (in the direction of the e
beam) would only see energies up to $E_{e}=60$ GeV. The size of the detector
corresponds to about that of CMS at the LHC.

Special runs are possible at much lower yet still sizeable luminosity, such as
with reduced beam energies. There is also the important programme of electron-
ion scattering which extended the kinematic range of the previous lepton-
nucleus experiments by 4 orders of magnitude. This is bound to revolutionise
the understanding of parton dynamics and substructure of nuclei and it will
shed light on the understanding of the formation and development of the Quark-
Gluon Plasma.

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