Nonlinear model predictive control of legged robots with accelerated first-order optimization

This paper presents an accelerated first-order approach for solving nonlinearly constrained, nonconvex model predictive control (MPC) problems in legged robots. The proposed method employs a nonmonotone Accelerated Projected Gradient (APG) algorithm with Nesterov momentum and backtracking line search, relying only on gradient information and closed-form projection operators. This enables efficient handling of typical control constraints, such as friction cones and box constraints, without requiring Hessian or constraint derivative computations. Compared to a Sequential Quadratic Programming (SQP) baseline, the method achieves shorter computation times and lower objective values in the considered test scenarios, leading to improved tracking performance. Its low per-iteration computational cost enables real-time nonlinear MPC at 100 Hz on an embedded single-board computer with limited computational resources. The effectiveness of the proposed framework is validated through offline comparisons, real-time simulations, and experiments on a quadruped robot, as well as simulations on a biped system. These results demonstrate that the proposed approach provides an efficient and practical solution for real-time control of legged robots under nonlinear dynamics and control constraints within the evaluated scenarios.