Smooth and near time-optimal trajectory planning of robotic manipulator with smooth constraint based on cubic B-spline

Minimum time optimization trajectory planning problem which can generate smooth trajectory of joints of robot is still complex and difficult to solve. A novel hybrid cubic B-spline and convex optimization method was presented for trajectory planning of robotic manipulator in this paper. First, the first and second derivatives of path trajectory coordinates s, called pseudo-velocity and pseudo-acceleration respectively, are introduced into robot dynamic model, and consequently transformed the optimal trajectory problem into convex optimization problem. Then, to obtain a jerk-bounded smooth trajectory of manipulator joints, the cubic B-spline was employed to construct the curve of the square of pseudo-velocity as smooth constraint of the transformed convex optimization model. Also, the process of solving the time-optimal problem is presented. Finally, numerical simulation on a three-DOF (degree of freedom) robotic manipulator is carried out. The results demonstrate the effectiveness of smoothing the trajectory of joints of robot with the proposed method.