Generating Feasible Solutions for Dynamically Crossing a Wide Ditch by a Biped Robot

The aim of this research work is to generate feasible motion for a biped robot to dynamically cross a wide ditch which is defined as a ditch with width more than or equal to the leg length. We propose an approach to obtain feasible solutions for dynamically crossing the wide ditch considering the dynamic balance of the biped robot, friction between the robot foot and ground, impact on the foot, limitations on the joint actuator torques and angular velocities. The biped robot is modeled as a seven link planar robot with the ditch crossing task consisting of two single support phases and a double support phase. An algorithm is developed to find the joint trajectories and the joint torques in each phase of ditch crossing by formulating the ditch crossing task as a constrained nonlinear optimization problem. In order to make the algorithm converge fast and to give feasible solutions, additional constraints called Adopted Constraints (ACs) are incorporated into the system of constraints. With time being one of the parameters, the developed algorithm adaptively adjusts the time for crossing a wide ditch. The significance of ground reaction force constraints in obtaining feasible solutions for crossing the wide ditch is shown through simulations. Feasible solutions obtained from simulation results provide not only the feasible joint angle trajectories, but also the joint torques required for the selection of actuators for a biped robot crossing the wide ditch.