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

Particle Computation: Complexity, Algorithms, and Logic

We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of obstacles to the environment can be used to create complex systems. We provide a wide range of results for a wide range of questions. These can be subdivided into external algorithmic problems, in which particle configurations serve as input for computations that are performed elsewhere, and internal logic problems, in which the particle configurations themselves are used for carrying out computations. For external algorithms, we give both negative and positive results. If we are given a set of stationary obstacles, we prove that it is NP-hard to decide whether a given initial configuration of unit-sized particles can be transformed into a desired target configuration. Moreover, we show that finding a control sequence of minimum length is PSPACE-complete. We also work on the inverse problem, providing constructive algorithms to design workspaces that efficiently implement arbitrary permutations between different configurations. For internal logic, we investigate how arbitrary computations can be implemented. We demonstrate how to encode dual-rail logic to build a universal logic gate that concurrently evaluates and, nand, nor, and or operations. Using many of these gates and appropriate interconnects, we can evaluate any logical expression. However, we establish that simulating the full range of complex interactions present in arbitrary digital circuits encounters a fundamental difficulty: a fan-out gate cannot be generated. We resolve this missing component with the help of 2x1 particles, which can create fan-out gates that produce multiple copies of the inputs. Using these gates we provide rules for replicating arbitrary digital circuits.Comment: 27 pages, 19 figures, full version that combines three previous conference article