Bipedal Robot Joint Trajectory Generation for Predetermined Zero Momentum Point

Numerous control methodologies have been proposed by researchers to develop an efficient bipedal dynamic walking robots that emulate human locomotion. In our previous works we have introduced Energy Dissipation Rate Control (EDRC) where a stable walking gait was achieved by regulating the rate of the energy dissipation, during each Impact Phases (IP). This method opposes previous works in this field where their core underlying approach revolves around modulating the robot's energy levels throughout each Single Support Phase (SSP). To ensure the stability of the biped robots, compliance with the Zero Momentum Point (ZMP) criterion is crucial. In this work, a new semi-analytical pattern generation approach is introduced to address this requirement. This new approach is capable of deriving all the robot's joint trajectories and torques by formulating the inverse kinematic and kinetic equations, along with ZMP criterion as a nonlinear state space system. For the first time in this work, it is shown how ZMP cause the coupling between the kinetic and kinematic equations which requires solving the inverse kinematic and kinetic equations simultaneously. Subsequently, this system of equation is solved by direct integration using Runge–Kutta method. Simulation results confirm the compatibility of the previously introduced EDRC method and the proposed semi-analytical pattern generation approach, as they can facilitate stable walking gait for biped robots.