Motion Planning for Vibration Reduction of a Railway Bridge Maintenance Robot with a Redundant Manipulator

Motivated by the potential applications of maintenance and inspection tasks for railway bridges, we have developed a biped climbing robot. The biped climbing robot can climb on the steel guardrail of the railway bridge with two electromagnetic feet and implement the maintenance and inspection tasks by a redundant manipulator with 7 degrees of freedom. To reduce the vibration of the manipulator caused by the low rigidity of the guardrail and the discontinuous trajectories of joints, a motion planning algorithm for vibration reduction is proposed in this paper. A geometric path accounting for obstacle avoidance and the manipulator’s center of gravity is determined by the gradient projection method with a singularity-robust inverse. Then, a piecewise quintic polynomial S shape curve with a smooth jerk (derivative of joint angular acceleration) profile is used to interpolate the sequence of joint angular position knots that are transformed from the via-points in the obstacle-avoidance path. The parameters of the quintic polynomial S-curve are determined by a nonlinear programming problem in which the objective function is to minimize the maximus of the torque exerted by the manipulator on the guardrail throughout the jerk-continuous trajectory. Finally, a series of simulation experiments are conducted to validate the effectiveness of the proposed algorithm. The simulation results show that the tracking errors of the trajectory with the proposed optimization algorithm are significantly smaller than the tracking errors of the trajectory without optimization. The absolute values of mean deviation of the tracking errors of the three coordinate axes decreased by at least 48.3% compared to the trajectory without vibration-reduction in the triangle working path and linear working path trajectory following simulations. The analysis results prove that the proposed algorithm can effectively reduce the vibration of the end effector of the manipulator.