Nonprehensile Manipulation of Deformable Objects: Achievements and Perspectives from the RoDyMan Project

The goal of this work is to disseminate the results achieved so far within the RODYMAN project related to planning and control strategies for robotic nonprehensile manipulation. The project aims at advancing the state of the art of nonprehensile dynamic manipulation of rigid and deformable objects to future enhance the possibility of employing robots in anthropic environments. The final demonstrator of the RODYMAN project will be an autonomous pizza maker. This article is a milestone to highlight the lessons learned so far and pave the way towards future research directions and critical discussions

Data-Driven Design of Energy-Shaping Controllers for Swing-Up Control of Underactuated Robots

We propose a novel data-driven procedure to train a neural network for the swing-up control of underactuated robotic systems. Our approach is inspired by several recent developments ranging from nonlinear control theory to machine learning. We embed a neural network indirectly into the equations of motion of the robotic manipulator as its control input. Using familiar results from passivity-based and energy-shaping control literature, this control function is determined by the appropriate gradients of a neural network, acting as an energy-like (Lyapunov) function. We encode the task of swinging-up robotic systems through the use of transverse coordinates and goal sets; which drastically accelerates the rate of learning by providing a concise target for the neural network. We demonstrate the efficacy of the algorithm with both numerical simulations and experiments

A Coordinate-Free Framework for Robotic Pizza Tossing and Catching

This chapter presents a solution to the problem of autonomous pizza tossing and catching. Under the assumption that robotic fingers grasp the pizza dough with soft contact, the grasp constraints are formulated and used to derive the individual and combined Euler-Lagrange dynamic equations of motion of the robotic manipulator and the dough. In particular, the dynamics of the dough is a modified version of the rigid-body dynamics, taking into account the change of inertia due to its deformation. Through these mathematical models, the two control problems of tossing and catching are formulated. For the tossing phase, an exponentially convergent controller that stabilizes a desired velocity of the dough as it leaves the fingers, is derived. On the other hand, to catch the dough, an optimal trajectory for the end-effector of the robotic manipulator is generated. Finally, the control laws to make the optimal trajectory exponentially attractive are derived. The developed theory is demonstrated with an elaborate simulation of the tossing and catching phases. This chapter is based on the work presented in [1]

Centralized and Decentralized Optimal Control of Variable Speed Heat Pumps

Utility service providers are often challenged with the synchronization of thermostatically controlled loads. Load synchronization, as a result of naturally occurring and demand-response events, has the potential to damage power distribution equipment. Because thermostatically controlled loads constitute most of the power consumed by the grid at any given time, the proper control of such devices can lead to significant energy savings and improved grid stability. The contribution of this paper is the development of an optimal control algorithm for commonly used variable speed heat pumps. By means of selective peer-to-peer communication, our control architecture allows for the regulation of home temperatures while simultaneously minimizing aggregate power consumption, and aggregate load volatility. An optimal centralized controller is also explored and compared against its decentralized counterpart

Nonholonomic Rolling Nonprehensile Manipulation Primitive

This chapter reviews the problem of nonholonomic rolling in nonprehen- sile manipulation tasks through two challenging and illustrative examples: the robotic hula-hoop and the ballbot system. The hula-hoop consists of an actuated stick and an unactuated hoop. First, the corresponding kinematic model is derived. Second, the dynamic model is derived through the Lagrange-D’Alembert equations. Then a control strategy is designed to rotate the hoop at some desired constant speed whereas positioning it over a desired point on the stick surface. A stability analysis, which guarantees ultimate boundedness of all signals of interest, is carried out. The ball-bot is an underactuated and nonholonomic constrained mobile robot whose upward equilibrium point must be stabilised by active controls. Coordinate-invariant equations of motion are derived for the ballbot. The linearised equations of motion are then derived, followed by the detailed controllability analysis. Excluding the rotary degree of freedom of the ball in the inertial vertical direction, the linear system turns out to be controllable. It follows that the nonlinear system is locally controllable, and a proportional-derivative type controller is designed to locally exponentially stabilise the upward equilibrium point and the translation of the ball. Numerical simulations for these two examples illustrate the effectiveness of the proposed methods. This chapter is based on the works presented in [1–4]

An Optimal Trajectory Planner for a Robotic Batting Task: The Table Tennis Example

This paper presents an optimal trajectory planner for a robotic batting task . The specific case of a table tennis game performed by a robot is considered. Given an estimation of the trajectory of the ball during the free flight, the method addresses the determination of the paddle configuration (pose and velocity) to return the ball at a desired position with a desired spin. The implemented algorithm takes into account the hybrid dynamic model of the ball in free flight as well as the state transition at the impact (the reset map). An optimal trajectory that minimizes the acceleration functional is generated for the paddle to reach the desired impact position, velocity and orientation. Simulations of different case studies further bolster the approach along with a comparison with state-of-the-art methods

Combining Energy-Shaping Control of Dynamical Systems with Data-Driven Approaches

Machine learning approaches to the problem of control design are flexible, but they demand large databases and computation time for training. Part of this central challenge is due to treating the environment as a black box, ignoring the useful geometric or algebraic structures of the control system. In this work, we propose an efficient data-driven procedure that leverages the known dynamics and techniques from nonlinear control theory in order to design swing-up controllers for underactuated robotic systems. We embed a neural network into the equations of motion of the robotic manipulator through its control input. This control function is determined by the appropriate gradients of a neural network, acting as an energy-like (Lyapunov) function. We encode the swing-up task through the use of transverse coordinates and goal sets; which provides a concise target for the neural network and drastically accelerates the rate of learning. We demonstrate the efficacy and robustness of the algorithm with numerical simulations and experiments on hardware

Nonholonomic Cooperative Manipulation in the Plane Using Linear Complementarity Formulation

This paper presents a framework in which a group of nonholonomic wheeled mobile robots are cooperatively utilized to manipulate a polygonal object in the plane. In this framework, the robots are assumed to contact the object without friction, applying forces normal to the object’s boundary. Contacts between the wheeled mobile robots and object are resolved through Moreau’s time stepping algorithm with a linear complementarity problem. The robots are controlled so that the object’s pose is asymptotically stabilized without the need for trajectory planning. Lastly, a recovery controller is proposed that places agents on the boundary of the object with a force closure grasp. An extensive simulation study is presented to support the proposed framework

Robustness of Control Design via Bayesian Learning

In the realm of supervised learning, Bayesian learning has shown robust predictive capabilities under input and parameter perturbations. Inspired by these findings, we demonstrate the robustness properties of Bayesian learning in the control search task. We seek to find a linear controller that stabilizes a one-dimensional open-loop unstable stochastic system. We compare two methods to deduce the controller: the first (deterministic) one assumes perfect knowledge of system parameter and state, the second takes into account uncertainties in both and employs Bayesian learning to compute a posterior distribution for the controller

Robust Data-Driven Passivity-Based Control of Underactuated Systems via Neural Approximators and Bayesian Inference

We synthesize controllers for underactuated robotic systems using data-driven approaches. Inspired by techniques from classical passivity theory, the control law is parametrized by the gradient of an energy-like (Lyapunov) function, which is represented by a neural network. With the control task encoded as the objective of the optimization, we systematically identify the optimal neural net parameters using gradient-based techniques. The proposed method is validated on the cart-pole swing-up task, both in simulation and on a real system. Additionally, we address questions about controller’s robustness against model uncertainties and measurement noise, using a Bayesian approach to infer a probability distribution over the parameters of the controller. The proposed robustness improvement technique is demonstrated on the simple pendulum system