Benchmarking Different QP Formulations and Solvers for Dynamic Quadrupedal Walking

Quadratic Programs (QPs) are widely used in the control of walking robots, especially in Model Predictive Control (MPC) and Whole-Body Control (WBC). In both cases, the controller design requires the formulation of a QP and the selection of a suitable QP solver, both requiring considerable time and expertise. While computational performance benchmarks exist for QP solvers, studies comparing optimal combinations of computational hardware (HW), QP formulation, and solver performance are lacking. In this work, we compare dense and sparse QP formulations, and multiple solving methods on different HW architectures, focusing on their computational efficiency in dynamic walking of four-legged robots using MPC. We introduce the Solve Frequency per Watt (SFPW) as a performance measure to enable a cross-hardware comparison of the efficiency of QP solvers. We also benchmark different QP solvers for WBC that we use for trajectory stabilization in quadrupedal walking. As a result, this paper recommends a starting point for practitioners on the selection of QP formulations and solvers for different HW architectures in walking robots and indicates which problems should be devoted the greater technical effort.