Efficient Cartesian path approximation for robots using trigonometric splines

A smooth approximation of a desired robot path can be realized by interpolating a sequence of joint-space knots with a trigonometric spline. In this paper we derive the computational effort required for the formulation of trigonometric splines and show how real-time obstacle avoidance can be implemented. The required computational expense is calculated and compared to that of algebraic splines. In addition, we demonstrate analytically that the Cartesian path error resulting from the use of trigonometric splines is inversely proportional to the number of knots if certain assumptions are satisfied. We then verify this result numerically, and extend the result numerically to cases where the given assumptions are not satisfied.