Parameterizable and Jerk-Limited Trajectories with Blending for Robot Motion Planning and Spherical Cartesian Waypoints

This paper presents two different approaches to generate a time local-optimal and jerk-limited trajectory with blends for a robot manipulator under consideration of kinematic constraints. The first approach generates a trajectory with blends based on the trapezoidal acceleration model by formulating the problem as a nonlinear constraint and a non-convex optimization problem. The resultant trajectory is locally optimal and approximates straight-line movement while satisfying the robot manipulator's constraints. We apply the bridged optimization strategy to reduce the computational complexity, which borrows an idea from model predictive control by dividing all waypoints into consecutive batches with an overlap of multiple waypoints. We successively optimize each batch. The second approach is a combination of a trapezoidal acceleration model with a 7-degree polynomial to form a path with blends. It can be efficiently computed given the specified blending parameters. The same approach is extended to Cartesian space. Furthermore, a quaternion interpolation with a high degree polynomial under consideration of angular kinematics is introduced. Multiple practical scenarios and trajectories are tested and evaluated against other state-of-the-art approaches.