Optimization-Based Control for Dynamic Legged Robots

In a world designed for legs, quadrupeds, bipeds, and humanoids have the opportunity to impact emerging robotics applications from logistics, to agriculture, to home assistance. The goal of this survey is to cover the recent progress toward these applications that have been driven by model-based optimization for the real-time generation and control of movement. The majority of the research community has converged on the idea of generating locomotion control laws by solving an optimal control problem (OCP) in either a model-based or data-driven manner. However, solving the most general of these problems online remains intractable due to complexities from intermittent unidirectional contacts with the environment, and from the many degrees of freedom of legged robots. This survey covers methods that have been pursued to make these OCPs computationally tractable, with a specific focus on how environmental contacts are treated, how the model can be simplified, and how these choices affect the numerical solution methods employed. The survey focuses on model-based optimization while paving its way for broader combination with learning-based formulations to accelerate progress in this growing field.

I. Introduction

Over the past decade, we have witnessed rapid growth in the capabilities of legged robots, transitioning from a state of the art where only a few research groups had access to capable platforms, to one where robust locomotion is now common in industry and academic laboratories. This rapid progress has been enabled by a combination of advances across design and control, with optimization-based control strategies playing a central role in many of the milestone demonstrations during this period (Fig. 1). Through these advances, current bipeds, quadrupeds, and humanoids can now walk reliably in nominal environments, and these improved capabilities have led to the first practical deployments of legged systems (e.g., the robot spot from Boston Dynamics). In a world built for legs, the growing scope of these deployments offers a broad opportunity for impact on applications spanning logistics (e.g., delivery), agriculture, and home assistance, among many others.