Convex Optimization in Legged Robots

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. These advancements have the potential to revolutionize industries and help humans in daily life. Control problems can be formulated as optimization problems We start with some literature and initial works on convex by defining an objective function that quantifies the optimization applications in legged robots, which lay the desired behavior of the system, and a set of constraints that foundation to the most widely used optimization methods, capture the physical limitations of the system and any other Model Predictive Control.