Multiscale methods for high-dimensional optimal control and planning in robotics

Abstract

This thesis addresses optimal control and planning problems of high-dimensional robotic systems. First, a multiscale framework is proposed to solve a class of continuous-time, continuous-space stochastic optimal and inverse optimal control problems in a complex environment. For both settings, a principled hierarchical representation of the problem is obtained using the diffusion wavelet method. This representation is utilized to solve stochastic optimal and inverse optimal control problems, where the sequence of problems are solved from the coarsest approximation to the finest one. Also, the hierarchy allows for the multi-resolution solution of the problem. Combined with a receding-horizon scheme in execution of the optimal control solution, the proposed method can generate continuous control sequence for robot motion. In addition, to handle complications arising from the high-dimensionality (like 50+ dimensions), and to solve a corresponding motion planning problem efficiently, the idea of latent variable models are adopted. Specifically, the GP-LVM provides a low-dimensional stochastic dynamic model, which is combined with the probabilistic interpretation of the optimal control problem. The efficient inference algorithm based on the particle filter and dynamic programming algorithm is proposed to address the combined fully-probabilistic model. Finally, the multiscale approach that increases the computational efficiency of the proposed inference algorithm is also presented. Numerical demonstrations on synthetic toy examples, on quadrotor control problems, and on a motion planning of a humanoid robot, are given to show the validity and applicability of the proposed methods.