Fast pivoting gait generation by model predictive control designed with basis functions

Pivoting gait is an efficient way for robots to manipulate a heavy object. Although we can cope with the contact constraints of the pivoting gait by using the model predictive control (MPC), systems with complex dynamics, including the pivoting gait, usually require long horizons in the MPC and it leads to a heavy computational load. To overcome this problem, we introduce basis functions to parameterize the free variables in the MPC and formulate an optimization problem with new decision variables, which are coefficients of the basis functions. We especially introduce multiple basis functions and compare their performances in generating the robotic pivoting gait. As a result, the most effective reduction in the dimension of the free variables is achieved by using the Laguerre basis function and the computational efficiency of the MPC is greatly improved. The simulation and experiments show that the time cost of the generation of pivoting gaits by the proposed method is remarkably reduced and the generated pivoting gaits are feasible and robust where a dual-arm robot successfully manipulates a toy piano by the pivoting gait.