An Efficient Optimal Planning and Control Framework For Quadrupedal Locomotion

TL;DR

This paper introduces an efficient dynamic programming framework for optimal planning and control of quadrupedal robots, utilizing multi-level optimization and a continuous-time LQR algorithm to improve computational efficiency and performance across various locomotion tasks.

Contribution

It proposes a novel multi-level optimization approach for switched systems and a continuous-time LQR algorithm with O(n) complexity for quadrupedal robot control.

Findings

Effective optimization of contact forces and joint velocities for different gaits

Improved computational efficiency over traditional methods

Successful validation on a quadrupedal robot across multiple tasks

Abstract

In this paper, we present an efficient Dynamic Programing framework for optimal planning and control of legged robots. First we formulate this problem as an optimal control problem for switched systems. Then we propose a multi--level optimization approach to find the optimal switching times and the optimal continuous control inputs. Through this scheme, the decomposed optimization can potentially be done more efficiently than the combined approach. Finally, we present a continuous-time constrained LQR algorithm which simultaneously optimizes the feedforward and feedback controller with $O(n)$ time-complexity. In order to validate our approach, we show the performance of our framework on a quadrupedal robot. We choose the Center of Mass dynamics and the full kinematic formulation as the switched system model where the switching times as well as the contact forces and the joint velocities are optimized for different locomotion tasks such as gap crossing, walking and trotting.