Raffaello D'Andrea

Michael Muehlebach, Raffaello D'Andrea

This article describes an approach for parametrizing input and state trajectories in model predictive control. The parametrization is designed to be invariant to time shifts, which enables warm-starting the successive optimization problems and reduces the computational complexity of the online optimization. It is shown that in certain cases (e.g. for linear time-invariant dynamics with input and state constraints) the parametrization leads to inherent stability and recursive feasibility guarantees without additional terminal set constraints. Due to the fact that the number of decision variables are greatly reduced through the parametrization, while the warm-starting capabilities are preserved, the approach is suitable for applications where the available computational resources (memory and CPU-power) are limited.

Michael Muehlebach, Raffaello D'Andrea

By parametrizing input and state trajectories with basis functions different approximations to the constrained linear quadratic regulator problem are obtained. These notes present and discuss technical results that are intended to supplement a corresponding journal article. The results can be applied in a model predictive control context.

Antonio Terpin, Alan Bonomi, Francesco Banelli et al.

We describe SynthPix, a synthetic image generator for Particle Image Velocimetry (PIV) with a focus on performance and parallelism on accelerators, implemented in JAX. SynthPix supports the same configuration parameters as existing tools but achieves a throughput several orders of magnitude higher in image-pair generation per second. SynthPix was developed to enable the training of data-hungry reinforcement learning methods for flow estimation and for reducing the iteration times during the development of fast flow estimation methods used in recent active fluids control studies with real-time PIV feedback. We believe SynthPix to be useful for the fluid dynamics community, and in this paper we describe the main ideas behind this software package.

Francesco Banelli, Antonio Terpin, Alan Bonomi et al.

Flow Gym is a toolkit for research and deployment of flow-field quantification methods inspired by OpenAI Gym and Stable-Baselines3. It uses SynthPix as synthetic image generation engine and provides a unified interface for the testing, deployment and training of (learning-based) algorithms for flow-field quantification from a number of consecutive images of tracer particles. It also contains a growing number of integrations of existing algorithms and stable (re-)implementations in JAX.

Antonio Terpin, Raffaello D'Andrea

Many high-performance human activities are executed with little or no external feedback: think of a figure skater landing a triple jump, a pitcher throwing a curveball for a strike, or a barista pouring latte art. To study the process of skill acquisition under fully controlled conditions, we bypass human subjects. Instead, we directly interface a generalist reinforcement learning agent with a spinning cylinder in a tabletop circulating water channel to maximize or minimize drag. This setup has several desirable properties. First, it is a physical system, with the rich interactions and complex dynamics that only the physical world has: the flow is highly chaotic and extremely difficult, if not impossible, to model or simulate accurately. Second, the objective -- drag minimization or maximization -- is easy to state and can be captured directly in the reward, yet good strategies are not obvious beforehand. Third, decades-old experimental studies provide recipes for simple, high-performance open-loop policies. Finally, the setup is inexpensive and far easier to reproduce than human studies. In our experiments we find that high-dimensional flow feedback lets the agent discover high-performance drag-control strategies with only minutes of real-world interaction. When we later replay the same action sequences without any feedback, we obtain almost identical performance. This shows that feedback, and in particular flow feedback, is not needed to execute the learned policy. Surprisingly, without flow feedback during training the agent fails to discover any well-performing policy in drag maximization, but still succeeds in drag minimization, albeit more slowly and less reliably. Our studies show that learning a high-performance skill can require richer information than executing it, and learning conditions can be kind or wicked depending solely on the goal, not on dynamics or policy complexity.

Thomas Bi, Raffaello D'Andrea

Motivated by the challenge of achieving rapid learning in physical environments, this paper presents the development and training of a robotic system designed to navigate and solve a labyrinth game using model-based reinforcement learning techniques. The method involves extracting low-dimensional observations from camera images, along with a cropped and rectified image patch centered on the current position within the labyrinth, providing valuable information about the labyrinth layout. The learning of a control policy is performed purely on the physical system using model-based reinforcement learning, where the progress along the labyrinth's path serves as a reward signal. Additionally, we exploit the system's inherent symmetries to augment the training data. Consequently, our approach learns to successfully solve a popular real-world labyrinth game in record time, with only 5 hours of real-world training data.

Panagiotis D. Grontas, Antonio Terpin, Efe C. Balta et al.

We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $Π$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $Π$net as a feasible-by-design optimization proxy for parametric constrained optimization problems and obtain modest-accuracy solutions faster than traditional solvers when solving a single problem, and significantly faster for a batch of problems. We surpass state-of-the-art learning approaches in terms of training time, solution quality, and robustness to hyperparameter tuning, while maintaining similar inference times. Finally, we tackle multi-vehicle motion planning with non-convex trajectory preferences and provide $Π$net as a GPU-ready package implemented in JAX with effective tuning heuristics.

Pietro Griffa, Carmelo Sferrazza, Raffaello D'Andrea

Grasping objects whose physical properties are unknown is still a great challenge in robotics. Most solutions rely entirely on visual data to plan the best grasping strategy. However, to match human abilities and be able to reliably pick and hold unknown objects, the integration of an artificial sense of touch in robotic systems is pivotal. This paper describes a novel model-based slip detection pipeline that can predict possibly failing grasps in real-time and signal a necessary increase in grip force. As such, the slip detector does not rely on manually collected data, but exploits physics to generalize across different tasks. To evaluate the approach, a state-of-the-art vision-based tactile sensor that accurately estimates distributed forces was integrated into a grasping setup composed of a six degrees-of-freedom cobot and a two-finger gripper. Results show that the system can reliably predict slip while manipulating objects of different shapes, materials, and weights. The sensor can detect both translational and rotational slip in various scenarios, making it suitable to improve the stability of a grasp.

Yaohui Huang, Matthias Hofer, Raffaello D'Andrea

This paper presents an offset-free model predictive controller for fast and accurate control of a spherical soft robotic arm. In this control scheme, a linear model is combined with an online disturbance estimation technique to systematically compensate model deviations. Dynamic effects such as material relaxation resulting from the use of soft materials can be addressed to achieve offset-free tracking. The tracking error can be reduced by 35% when compared to a standard model predictive controller without a disturbance compensation scheme. The improved tracking performance enables the realization of a ball catching application, where the spherical soft robotic arm can catch a ball thrown by a human.

Zheng Jia, Michael Hamer, Raffaello D'Andrea

In this thesis we are interested in applying distributed estimation, control and optimization techniques to enable a group of quadcopters to fly through openings. The quadcopters are assumed to be equipped with a simulated bearing and distance sensor for localization. Some quadcopters are designated as leaders who carry global position sensors. We assume quadcopters can communicate information with each other.

Thomas Bi, Carmelo Sferrazza, Raffaello D'Andrea

This paper aims to show that robots equipped with a vision-based tactile sensor can perform dynamic manipulation tasks without prior knowledge of all the physical attributes of the objects to be manipulated. For this purpose, a robotic system is presented that is able to swing up poles of different masses, radii and lengths, to an angle of 180 degrees, while relying solely on the feedback provided by the tactile sensor. This is achieved by developing a novel simulator that accurately models the interaction of a pole with the soft sensor. A feedback policy that is conditioned on a sensory observation history, and which has no prior knowledge of the physical features of the pole, is then learned in the aforementioned simulation. When evaluated on the physical system, the policy is able to swing up a wide range of poles that differ significantly in their physical attributes without further adaptation. To the authors' knowledge, this is the first work where a feedback policy from high-dimensional tactile observations is used to control the swing-up manipulation of poles in closed-loop.

Carmelo Sferrazza, Raffaello D'Andrea

The images captured by vision-based tactile sensors carry information about high-resolution tactile fields, such as the distribution of the contact forces applied to their soft sensing surface. However, extracting the information encoded in the images is challenging and often addressed with learning-based approaches, which generally require a large amount of training data. This article proposes a strategy to generate tactile images in simulation for a vision-based tactile sensor based on an internal camera that tracks the motion of spherical particles within a soft material. The deformation of the material is simulated in a finite element environment under a diverse set of contact conditions, and spherical particles are projected to a simulated image. Features extracted from the images are mapped to the 3D contact force distribution, with the ground truth also obtained via finite-element simulations, with an artificial neural network that is therefore entirely trained on synthetic data avoiding the need for real-world data collection. The resulting model exhibits high accuracy when evaluated on real-world tactile images, is transferable across multiple tactile sensors without further training, and is suitable for efficient real-time inference.

Matthias Hofer, Carmelo Sferrazza, Raffaello D'Andrea

Sensory feedback is essential for the control of soft robotic systems and to enable deployment in a variety of different tasks. Proprioception refers to sensing the robot's own state and is of crucial importance in order to deploy soft robotic systems outside of laboratory environments, i.e. where no external sensing, such as motion capture systems, is available. A vision-based sensing approach for a soft robotic arm made from fabric is presented, leveraging the high-resolution sensory feedback provided by cameras. No mechanical interaction between the sensor and the soft structure is required and consequently, the compliance of the soft system is preserved. The integration of a camera into an inflatable, fabric-based bellow actuator is discussed. Three actuators, each featuring an integrated camera, are used to control the spherical robotic arm and simultaneously provide sensory feedback of the two rotational degrees of freedom. A convolutional neural network architecture predicts the two angles describing the robot's orientation from the camera images. Ground truth data is provided by a motion capture system during the training phase of the supervised learning approach and its evaluation thereafter. The camera-based sensing approach is able to provide estimates of the orientation in real-time with an accuracy of about one degree. The reliability of the sensing approach is demonstrated by using the sensory feedback to control the orientation of the robotic arm in closed-loop.

Jasan Zughaibi, Matthias Hofer, Raffaello D'Andrea

This paper presents the application of a learning control approach for the realization of a fast and reliable pick-and-place application with a spherical soft robotic arm. The arm is characterized by a lightweight design and exhibits compliant behavior due to the soft materials deployed. A soft, continuum joint is employed, which allows for simultaneous control of one translational and two rotational degrees of freedom in a single joint. This allows us to axially approach and pick an object with the attached suction cup during the pick-and-place application. A control allocation based on pressure differences and the antagonistic actuator configuration is introduced, allowing decoupling of the system dynamics and simplifying the modeling and control. A linear parameter-varying model is identified, which is parametrized by the attached load mass and a parameter related to the joint stiffness. A gain-scheduled feedback controller is proposed, which asymptotically stabilizes the robotic system for aggressive tuning and over large variations of the parameters considered. The control architecture is augmented with an iterative learning control scheme enabling accurate tracking of aggressive trajectories involving set point transitions of 60 degrees within 0.3 seconds (no mass attached) to 0.6 seconds (load mass attached). The modeling and control approach proposed results in a reliable realization of a pick-and-place application and is experimentally demonstrated.

Carmelo Sferrazza, Thomas Bi, Raffaello D'Andrea

Data-driven approaches to tactile sensing aim to overcome the complexity of accurately modeling contact with soft materials. However, their widespread adoption is impaired by concerns about data efficiency and the capability to generalize when applied to various tasks. This paper focuses on both these aspects with regard to a vision-based tactile sensor, which aims to reconstruct the distribution of the three-dimensional contact forces applied on its soft surface. Accurate models for the soft materials and the camera projection, derived via state-of-the-art techniques in the respective domains, are employed to generate a dataset in simulation. A strategy is proposed to train a tailored deep neural network entirely from the simulation data. The resulting learning architecture is directly transferable across multiple tactile sensors without further training and yields accurate predictions on real data, while showing promising generalization capabilities to unseen contact conditions.

Camill Trueeb, Carmelo Sferrazza, Raffaello D'Andrea

This paper describes the design of a multi-camera optical tactile sensor that provides information about the contact force distribution applied to its soft surface. This information is contained in the motion of spherical particles spread within the surface, which deforms when subject to force. The small embedded cameras capture images of the different particle patterns that are then mapped to the three-dimensional contact force distribution through a machine learning architecture. The design proposed in this paper exhibits a larger contact surface and a thinner structure than most of the existing camera-based tactile sensors, without the use of additional reflecting components such as mirrors. A modular implementation of the learning architecture is discussed that facilitates the scalability to larger surfaces such as robotic skins.

Peter Werner, Matthias Hofer, Carmelo Sferrazza et al.

This paper presents a vision-based sensing approach for a soft linear actuator, which is equipped with an integrated camera. The proposed vision-based sensing pipeline predicts the three-dimensional position of a point of interest on the actuator. To train and evaluate the algorithm, predictions are compared to ground truth data from an external motion capture system. An off-the-shelf distance sensor is integrated in a similar actuator and its performance is used as a baseline for comparison. The resulting sensing pipeline runs at 40 Hz in real-time on a standard laptop and is additionally used for closed loop elongation control of the actuator. It is shown that the approach can achieve comparable accuracy to the distance sensor.

Carmelo Sferrazza, Adam Wahlsten, Camill Trueeb et al.

Skin-like tactile sensors provide robots with rich feedback related to the force distribution applied to their soft surface. The complexity of interpreting raw tactile information has driven the use of machine learning algorithms to convert the sensory feedback to the quantities of interest. However, the lack of ground truth sources for the entire contact force distribution has mainly limited these techniques to the sole estimation of the total contact force and the contact center on the sensor's surface. The method presented in this article uses a finite element model to obtain ground truth data for the three-dimensional force distribution. The model is obtained with state-of-the-art material characterization methods and is evaluated in an indentation setup, where it shows high agreement with the measurements retrieved from a commercial force-torque sensor. The proposed technique is applied to a vision-based tactile sensor, which aims to reconstruct the contact force distribution purely from images. Thousands of images are matched to ground truth data and are used to train a neural network architecture, which is suitable for real-time predictions.

Matthias Hofer, Lukas Spannagl, Raffaello D'Andrea

This paper presents the application of an iterative learning control scheme to improve the position tracking performance for an articulated soft robotic arm during aggressive maneuvers. Two antagonistically arranged, inflatable bellows actuate the robotic arm and provide high compliance while enabling fast actuation. Switching valves are used for pressure control of the soft actuators. A norm-optimal iterative learning control scheme based on a linear model of the system is presented and applied in parallel with a feedback controller. The learning scheme is experimentally evaluated on an aggressive trajectory involving set point shifts of 60 degrees within 0.2 seconds. The effectiveness of the learning approach is demonstrated by a reduction of the root-mean-square tracking error from 13 degrees to less than 2 degrees after applying the learning scheme for less than 30 iterations.

Carmelo Sferrazza, Raffaello D'Andrea

Due to the complexity of modeling the elastic properties of materials, the use of machine learning algorithms is continuously increasing for tactile sensing applications. Recent advances in deep neural networks applied to computer vision make vision-based tactile sensors very appealing for their high-resolution and low cost. A soft optical tactile sensor that is scalable to large surfaces with arbitrary shape is discussed in this paper. A supervised learning algorithm trains a model that is able to reconstruct the normal force distribution on the sensor's surface, purely from the images recorded by an internal camera. In order to reduce the training times and the need for large datasets, a calibration procedure is proposed to transfer the acquired knowledge across multiple sensors while maintaining satisfactory performance.

Michael Muehlebach, Raffaello D'Andrea

These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a finite dimensional representation of the dynamics is obtained via a Galerkin approach. It is shown that the two approximations provide lower, respectively upper bounds on the optimal cost of the underlying infinite dimensional optimal control problem. These bounds get tighter as the number of basis functions is increased. In addition, conditions guaranteeing convergence to the cost of the underlying problem are provided.