Boundedness issues in planning of locomotion trajectories for biped robots

It is in general complex to consider the complete robot dynamics when planning trajectories for bipedal locomotion. We present an approach to trajectory planning, with the classical Linear Inverted Pendulum Model (LIPM), that takes explicit consideration of the unstable dynamics. We derive a relationship between initial state and the control input that ensures the overall system dynamics will converge to a stable steady state solution. This allows us to exploit the unstable dynamics to achieve system goals, while imposing constraints on certain degrees of freedom of the input and initial conditions. Based on this, we propose an approach to trajectory planning, and derive solutions for several typical applications. Experimental simulations using the REEM-C biped robot platform of Pal Robotics validate our approach.