A Novel Superlinearly Convergent Trust Region-Sequential Quadratic Programming Approach for Optimal Gait of Bipedal Robots Via Nonlinear Model Predictive Control

A type of trust region-sequential quadratic programming (TRSQP) approach with superlinearly convergent property is first proposed, investigated, and implemented on bipedal robots based on nonlinear model predictive control (NMPC). NMPC is utilized to predict the system behavior and optimize the control move in a receding horizon way, which will result in recursive efficiency and stability. Considering that the classical line search rules are expensive or hard in particular applications, the attempted trust region search is leveraged to avoid the drawbacks of the classical line search rules. Moreover, the feasible descent direction is contained in the trust region via a novelly truncated technique which avoids to recompute the quadratic programming subproblem (QPS) for the main search direction. Owing to some suitable conditions, the globally/superlinearly convergent performance and well-defined properties are analyzed and verified for the TRSQP. The main result is illustrated on a simple bipedal robot which is called as compass-like bipedal robot (CLBR) through numerical simulations and is used to generate dynamic locomotion via TRSQP and NMPC. Furthermore, to demonstrate the feasibility and superiority of a complex bipedal robot which is called as a high-dimensional bipedal robot, numerical simulations are conducted on the model of a three-link bipedal robot (TLBR) and a five-link robot (RABBIT). Furthermore, simulation results show that the TRSQP approach is effectiveness and superiority through comparing with the classical approaches, which included discrete mechanics and optimal control (DMOC) and hybrid zero dynamic (HZD), and control Lyapunov function-quadratic programming (CLF-QP) for the optimal gait of bipedal robot. In addition, to verify the robustness, the TLBR model with parameter’s disturbance 1.5 times is investigated and analyzed via TRSQP with NMPC technique. Last,this study develops an interesting framework to exploiting control methods on bipedal robots through accurately and effectively solving nonlinear programming problems.