Optimal LQR Controller Design for Wheel Legged Robots Using Genetic Algorithm

Abstract

Wheel-legged robots are typical nonlinear underactuated systems, whose balance control is commonly achieved by a Linear Quadratic Regulator (LQR). However, the performance of the LQR controller for such robots heavily depends on the selection of the state weighting matrix Q and the control weighting matrix R, which in practice relies highly on expert heuristics and often fails to achieve an efficient trade-off among multiple performance objectives. To address this issue, this paper proposes a systematic automatic tuning method for LQR controllers of wheel-legged robots. By embedding engineering constraints into the fitness function in the form of penalty terms, the proposed method can stably generate feasible controllers that achieve favorable multi-performance trade-offs without manual trial‑and‑error. On this basis, for variable leg‑length conditions, a grid‑based offline solution of the Riccati equation combined with polynomial fitting is employed to extend the optimal weightings obtained at the nominal leg length to the entire leg‑length range via gain scheduling, enabling online continuous adaptation of the feedback gain with respect to leg length. Simulation results on a nonlinear model demonstrate that the controller automatically optimized by the genetic algorithm (GA) exhibits good dynamic response and robustness under various scenarios, including balancing control, fall recovery, and terrain adaptation, thereby validating the effectiveness of the proposed method.