Computation of Feedback Control Laws Based on Switched Tracking of Demonstrations

TL;DR

This paper introduces an algorithm that synthesizes feedback control laws by switching between demonstration trajectories, offering a simpler and more efficient alternative to trajectory optimization-based control methods.

Contribution

The paper presents a novel algorithm that automatically generates feedback controllers from demonstrations with proven convergence and optimality, improving efficiency over existing methods.

Findings

Algorithm achieves rigorous convergence and optimality.

Computational experiments confirm efficiency and practicality.

Switching control laws simplify implementation compared to trajectory optimization.

Abstract

A common approach in robotics is to learn tasks by generalizing from special cases given by a so-called demonstrator. In this paper, we apply this paradigm and present an algorithm that uses a demonstrator (typically given by a trajectory optimizer) to automatically synthesize feedback controllers for steering a system described by ordinary differential equations into a goal set. The resulting feedback control law switches between the demonstrations that it uses as reference trajectories. In comparison to the direct use of trajectory optimization as a control law, for example, in the form of model predictive control, this allows for a much simpler and more efficient implementation of the controller. The synthesis algorithm comes with rigorous convergence and optimality results, and computational experiments confirm its efficiency.