Nonlinear Optimal Control of the Underactuated Wheeled Bipedal Robot

Wheeled bipedal robots are used in several civilian and defense tasks. In this paper, a new nonlinear optimal control method is proposed for solving the problem of control and stabilization of the 3-DOF wheeled bipedal robot. The control problem is nontrivial due to nonlinearities, and underactuation which affect the dynamic model of this robot. To apply the proposed nonlinear optimal control method, the dynamic model of the wheeled bipedal robot undergoes first approximate linearization around a temporary operating point that is updated at each iteration of the control algorithm. The linearization takes place through first-order Taylor series expansion and through the computation of the Jacobian matrices of the system's state-space description. For the approximately linearized model of the robot, an H-infinity feedback controller is designed. Actually, the H-infinity controller stands for the solution of the optimal control problem for the wheeled bipedal robot under uncertainty and external perturbations. For the computation of the feedback gains of the H-infinity controller, an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control algorithm are proven through Lyapunov analysis. First, it is shown that the control scheme achieves H-infinity tracking performance which signifies elevated robustness for the control loop of this robotic system under uncertainties and external perturbations. Next, it is also shown that the control loop of the wheeled bipedal robot is globally asymptotically stable. The proposed control method achieves fast and accurate tracking of setpoints under moderate variations of the control inputs.