Planning Adaptive Brachistochrone and Circular Arc Hip Trajectory for a Toe-Foot Bipedal Robot going Downstairs

Abstract

A novel efficient downstairs trajectory is proposed for a 9 link biped robot model with toe-foot. Trajectory of hip joint plays a significant role towards stability of the robot reason being the center of mass which lies approximately close to the hip position. Brachistochrone is the fastest descent trajectory for a particle moving only under the influence of gravity. In case of downstairs movement of robot, methodology for brachistochrone and circular arc trajectories for hip joint is developed. Here, an adaptive trajectory planning algorithm is implemented along with unsupervised artificial neural network (UANN) based inverse kinematics solution, so that biped robots of varying link lengths, masses can climb down on varying staircase dimensions. Zero Moment Point (ZMP) based COG trajectory is considered and its stability is ensured. Cycloidal trajectory is considered for ankle of the swing leg. Parameters of both cycloid and brachistochrone depends on dimensions of staircase steps. Hence this paper can be broadly divided into 4 steps 1) Developing ZMP based brachistochrone and circular arc trajectory for hip 2) Cycloidal trajectory planning for ankle by taking proper collision constraints 3) Solving Inverse kinematics using UANN 4) Comparison between both proposed hip trajectories. The proposed algorithms have been implemented using MATLAB®.