Convex Optimization in Legged Robots

TL;DR

This paper reviews how convex optimization techniques, especially SOCP, are applied to control and stabilize legged robots, improving their robustness, efficiency, and ability to perform complex tasks.

Contribution

It presents a general framework for formulating active balancing problems as SOCP and discusses their application to real-world robot stabilization tasks.

Findings

SOCP formulation enhances robustness and efficiency in control.

Feedback MPC improves prediction accuracy and reduces computational costs.

Application to jumping and landing demonstrates practical stabilization benefits.

Abstract

Convex optimization is crucial in controlling legged robots, where stability and optimal control are vital. Many control problems can be formulated as convex optimization problems, with a convex cost function and constraints capturing system dynamics. Our review focuses on active balancing problems and presents a general framework for formulating them as second-order cone programming (SOCP) for robustness and efficiency with existing interior point algorithms. We then discuss some prior work around the Zero Moment Point stability criterion, Linear Quadratic Regulator Control, and then the feedback model predictive control (MPC) approach to improve prediction accuracy and reduce computational costs. Finally, these techniques are applied to stabilize the robot for jumping and landing tasks. Further research in convex optimization of legged robots can have a significant societal impact. It can lead to improved gait planning and active balancing which enhances their ability to navigate complex environments, assist in search and rescue operations and perform tasks in hazardous environments. These advancements have the potential to revolutionize industries and help humans in daily life.