The Cubic B-spline Trajectories with the Boundary Conditions of Null Velocities and Accelerations

As for the pick-and-place operations (PPO), a robotic arm takes a workpiece from a given pose to a final pose. It is necessary to produce null velocities and accelerations at the ends. Furthermore, the cubic spline curves are computationally efficient and have narrower local support than higher-order B-splines. This paper presents a new approach to obtain null initial and final velocities and accelerations using the cubic B-spline curves. In our procedure, the approach only requires adding two “dummy” points into the original path nodes and maintains a linear system similar to solving the velocity or acceleration boundary conditions separately. The simulation results show that continuous and smooth trajectories can be generated by using our approach.