Nonlinear optimal control for three-link biped robots

This paper proposes a nonlinear optimal control approach for the three-link biped robot. In this humanoid robot there is actuation only in the two legs while the third link which is the robot’s torso is unactuated. Due to nonlinearities and the unactuated torso in the robot’s dynamics, the treatment of the stabilization and trajectories tracking problem is a non-trivial task. To solve the associated nonlinear optimal control problem, the state-space model of the three-link biped robot undergoes approximate linearization based on Taylor series expansion and the associated Jacobian matrices. For the linearized state-space model of the biped robot a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller’s feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis.