College of Arts and Sciences Application of Sampling-Based Model Predictive Control to Motion Planning for Robotic Manipulators

This thesis presents the Sampling-Based Model Predictive Control (SBMPC) Algorithm, a novel sampling-based planning algorithm. This algorithm was originally designed for dynamic system which are described by a set of system states and a sequence of control inputs that drive their evolution; however, this thesis reviews the applications of SBMPC to motion planning for robotic manipulators using kinematic models and kinematic models plus integrators (also referred to as extended kinematic models). To properly evaluate SBMPC, first a brief survey of conventional motion planning techniques used for manipulators is presented. This survey includes a comparison between combinatorial and sampling-based path planning algorithms as well as an overview of two recent sampling-based path planning algorithms: Rapidly Exploring Random Trees (RRTs) and Randomized A* (RA*). Once this preliminary information is discussed, a detail explanation of SBMPC and its components is presented. SBMPC actually combines four main components: an A*-type algorithm used for optimization, sampling of the control inputs, discretization of the system states, and the concept of a system model, whose purpose is to predict the new system state, given the current system states and a new set of control inputs. Next, results for some experiments done with SBMPC are presented. More specifically, SBMPC was used with simulations of two manipulators, namely a 3-link planar manipulator and the Barrett WAM. The results show that SBMPC can be used to generate smooth paths for these two manipulators simply by sampling joint velocities instead of joint angles, and even smoother paths by sampling joint accelerations instead of joint velocities. The results also demonstrate that SBMPC can generate smooth trajectories given that the proper cost function and goal heuristic are used. Since SBMPC is able to generate smooth smooth paths or smooth trajectories in a single step, this presents a significant improvement to the conventional approach used for robot motion ...