Coordinated nonprehensile manipulation for parts transfer: Mechanics, control, and planning

This thesis focuses on coordinated nonprehensile manipulation to accomplish a parts transfer task. Parts transfer refers to moving parts from a known initial configuration (position and orientation) to a goal configuration. This task is motivated by automatic manufacturing applications. The problem is studied under quasi-static and dynamic settings. By exploring the task mechanics and geometry, three nonprehensile (graspless) manipulation methods are developed. This thesis describes their mechanics, control and planning algorithms. The first part of the thesis investigates quasi-static cooperative nonprehensile manipulation. Two methods are studied for the parts transfer task. The problems of controllability and planning are studied for these methods. The aim of controllability is to determine whether the goal configuration of the part is reachable by cooperative nonprehensile manipulation, and the objective of planning is to find a cooperative motion (or action) of the agents to bring the part to the goal configuration. The first system demonstrates that a fixed-radius rotational push and a linear normal push are sufficient to manipulate an object in the plane. By using optimal control theory, a planner is developed to find the optimal solution. In the second system, new manipulation primitives such as, equilibrium push and non-equilibrium push, are introduced for manipulating convex parts. We prove the configuration controllability of the object under these pushes. A fully analytical planner is developed to solve the optimal sequence. Simulations and experiments are conducted to demonstrate the proposed manipulation methods. The second part of the thesis investigates dynamic cooperative manipulation. The motion of the object under manipulation consists of two phases: acceleration by cooperative dynamic pushing, and free sliding with initial velocity. For the free sliding problem, a free boundary value problem formulation (FBVP) is developed to find the desired release velocity. After transforming the FBVP into a two-point boundary value problem, a set of algorithms is developed to solve the planning problem. A degree of freedom mechanism is implemented to demonstrate the planning method. For the cooperative dynamic pushing problem, a centralized planning method is developed by integration of the backstepping design and quadratic programming under the known pressure distribution assumption. A game theoretic approach is proposed to solve the acceleration problem in the case of uncertain pressure distribution.