Nonprehensile Manipulation of an Underactuated Mechanical System With Second-Order Nonholonomic Constraints: The Robotic Hula-Hoop

A mechanical system consisting of a hoop and a pole is considered, for which the corresponding dynamic model represents an underactuated system subject to second-order nonholonomic constraints. The pursued goal is to simultaneously track a trajectory in the unactuated coordinates and to stabilize the actuated ones. For the model under consideration, the well-known noncollocated partial feedback linearization algorithm fails since the corresponding zero dynamics is unstable. In this work, we show that the actuated coordinates, i.e., the pole can be stabilized by exploiting the null space of the coupling inertia matrix without affecting the performance in the underactuated coordinates tracking. We present a formal mathematical analysis, which guarantees ultimate boundedness of all coordinates. Performed simulations bolster the proposed approach

Control of Nonprehensile Planar Rolling Manipulation: A Passivity-Based Approach

This paper presents a new procedure to design a control law using the classical interconnection and damping assignment technique within the passivity-based port-Hamiltonian framework. The sought goal is to reduce the complexity of solving the so-called matching equations. The proposed approach is applied to two case studies of planar rolling nonprehensile manipulation, namely, the ball-and-beam and the eccentric disk-on-disk. The performance of the resulting controllers is illustrated through both simulations and experimental results, showing the applicability of the design in a real setup

Nonprehensile Dynamic Manipulation: A Survey

Nonprehensile dynamic manipulation can be reason- ably considered as the most complex manipulation task. It might be argued that such a task is still rather far from being fully solved and applied in robotics. This survey tries to collect the results reached so far by the research community about planning and control in the nonprehensile dynamic manipulation domain. A discussion about current open issues is addressed as well

Closed-loop Control of a Nonprehensile Manipulation System Inspired by the Pizza-Peel Mechanism

A nonprehensile manipulation system consisting of a dexterous plate (e.g., a peel) which is intended to induce a rotating movement on a disk (e.g., a pizza) is studied. A dynamic model based on the Euler-Lagrange equations is first derived. Then, a controllability analysis of this model is carried out, which shows some intrinsic limitations of the proposed system. Later, a closed-loop control strategy is proposed to induce the desired rotating speed in the disk, while maintaining the position of both the disk and the plate as close to zero as possible. A stability analysis is performed to show the boundedness of all the states, the oscillatory response of all of them, and the maximum amplitude of these oscillations. A numerical simulation is employed to verify the proposed controller and the predicted behavior found in the stability analysis

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]

Interconnection and Damping Assignment Passivity-Based Control for Gait Generation in Underactuated Compass-Like Robots

A compass-like biped robot can go down a gentle slope without the need of actuation through a proper choice of its dynamic parameter and starting from a suitable initial condition. Addition of control actions is requested to generate additional gaits and robustify the existing one. This paper designs an interconnection and damping assignment passivity- based control, rooted within the port-Hamiltonian framework, to generate further gaits with respect to state-of-the-art methodologies, enlarge the basin of attraction of existing gaits, and further robustify the system against controller discretization and parametric uncertainties. The performance of the proposed algorithm is validated through numerical simulations and comparison with existing passivity-based techniques

Planning Framework for Robotic Pizza Dough Stretching with a Rolling Pin

Stretching a pizza dough with a rolling pin is a nonprehensile manipulation. Since the object is deformable, force closure cannot be established, and the manipulation is carried out in a nonprehensile way. The framework of this pizza dough stretching application that is explained in this chapter consists of four sub-procedures: (i) recognition of the pizza dough on a plate, (ii) planning the necessary steps to shape the pizza dough to the desired form, (iii) path generation for a rolling pin to execute the output of the pizza dough planner, and (iv) inverse kinematics for the bi-manual robot to grasp and control the rolling pin properly. Using the deformable object model described in Chap. 3, each sub-procedure of the proposed framework is explained sequentially

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

Reactive Planar Manipulation with Convex Hybrid MPC

This paper presents a reactive controller for planar manipulation tasks that leverages machine learning to achieve real-time performance. The approach is based on a Model Predictive Control (MPC) formulation, where the goal is to find an optimal sequence of robot motions to achieve a desired object motion. Due to the multiple contact modes associated with frictional interactions, the resulting optimization program suffers from combinatorial complexity when tasked with determining the optimal sequence of modes. To overcome this difficulty, we formulate the search for the optimal mode sequences offline, separately from the search for optimal control inputs online. Using tools from machine learning, this leads to a convex hybrid MPC program that can be solved in real-time. We validate our algorithm on a planar manipulation experimental setup where results show that the convex hybrid MPC formulation with learned modes achieves good closed-loop performance on a trajectory tracking problem