Motion planning for underactuated bipedal mechanisms with kinematic constraints

The motion planning for a bipedal robotic gait is studied in this paper in the light of its underactuated nature. The generation of motion trajectory and the corresponding actuation command for an underactuated mechanism is a challenging problem, especially when it is required to needs to satisfy a set of equalities forming kinematics constraints. Existing method that utilises forward dynamics approach is computationally expensive since the equation of motion, given the actuation command, needs to be integrated with respect to time prior to obtain the resulting motion before it can be tested against the kinematic constraints. In this paper, the use of virtual actuators on the unactuated joints is introduced and explored. The motion planning is performed by designing motion trajectories for the system that minimises the virtual actuator efforts. This approach was found to significantly increase the possibilities of obtaining admissible solutions and consequently, improves the computational efficiency. The implementation of the proposed method in searching for periodic gaits, optimised against a given cost function, for a simple underactuated bipedal mechanism is described in this paper. The approach was used to reproduce a well established previous study which was conducted on conventional approach and the outcomes were found to be consistent.