Trajectory Planning With Lamé-Curve Blending for Motor-Saturation Avoidance Upon Mobile-Robot Turning

In order to avoid motor saturation in turning maneuvers, an iterative Lamé-trajectory planning scheme is proposed to generate a smooth curvature-bounded transition trajectory for a differential-driving wheeled mobile robot (DWMR) switching from one straight path to another. The scheme consists of Lamécurve blending, inverse-kinematics computation, peak-torque positioning and torque-saturation avoidance. Firstly, a Lamé-curve blending procedure based on affine transformations, is formulated to generate a smooth G2-continuous transition trajectory for connecting two straight paths. Secondly, the platform twist is calculated according to the curvature of the Lamé-curve trajectory, then transformed into the actuated-joint rates by means of the inverse-kinematics model. Thirdly, a peak-torque positioning technique is developed to estimate the peak torques of the driving wheels when the DWMR tracks the trajectory, by combining the computed-torque method and the inverse-dynamics model. Finally, an iterative r-step saturation-avoidance prediction planning strategy is devised to suppress the peak motor torques, by means of two torque limitation schemes via adjusting trajectory curvature and robot speed. The simulation results show that, compared with the conventional planning techniques for circular arcs, our trajectory planning scheme can generate a smooth saturation-free transition trajectory with feasible curvature and traveling speed. The scheme is significantly beneficial for trajectory tracking under finite actuation torque in turning maneuvers, thereby preventing any possible path deviation caused by insufficient torque.