A Single-Step Optimization-Based Kinematic Controller for Real-Time Path Tracking of Legged Robots

Controlling the locomotion of autonomous legged robots requires sophisticated techniques to handle system constraints, often resulting in high computational demands that limit real-time implementation. This article presents a computationally efficient path tracking algorithm for legged robots, leveraging their kinematic model and built-in low-level motor control. Unlike traditional model predictive control (MPC), the proposed method simplifies the framework by using a single-step prediction window, achieving performance comparable to MPC with longer horizons, while significantly reducing computational overhead. Comparative analysis against a Nonlinear MPC with and without integral mode, a linear time-varying LQR, and a reinforcement learning agent demonstrates that the proposed algorithm achieves similar or superior tracking performance with much lower computational requirements and tuning. This makes the approach well-suited for real-time applications in resource-constrained robotic systems. In addition, the method facilitates fast prototyping for industrial applications, as performance and stability can be established using simple kinematic and path parameters. Our controller simplifies design requiring almost no tuning obtaining a similar performance in comparison with an NMPC with a control horizon of 20 sampling instant but with much less computational effort.