In this paper, methods based on various spline techniques for planning and fast modifications of a trajectory for robot manipulators are investigated. Algebraic and trigonometric splines, their combined use, and the use of the B-spline technique are analyzed and compared in detail. In so doing, we focus on the performance of sudden changes in a predefined trajectory, e.g. obstacle avoidance in real-time applications. Some comparative examples illustrate our results.

Interpolation of a robot joint trajectory is realized using trigonometric splines. This original application has several advantages over existing methods (e.g. those using algebraic splines). For example, the computational expense is lower, more constraints can be imposed on the trajectory, obstacle avoidance can be implemented in real time, and smoother trajectories are obtained. Some of the spline parameters can be chosen to minimize an objective function (e.g. minimum jerk or minimum energy). If jerk is minimized, the optimization has a closed form solution. This paper introduces a trajectory interpolation algorithm, discusses a method for path optimization, and includes examples.

In this paper, the use of algebraic and trigonometric splines for the trajectory planning of robot manipulators is discussed. First, the two methods are analyzed and compared in detail; then, a strategy, which involves a combined use of the two schemes to perform sudden changes in a predefined trajectory (e.g. in case of obstacle avoidance) is proposed. Results show that the main interest in using trigonometric splines lies especially in the task of connecting two separate pieces of cubic splines, as overshoots are significantly reduced, although the continuity of velocity, acceleration and (in case) jerk is guaranteed.