Computational Complexity and Path Error Analyses of Trigonometric Joint Trajectories

A smooth approximation of a desired robot path can be realized by interpolating a sequence of joint-space knots with a trigonometric spline. The authors 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, the authors 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. The authors then verify this result numerically and extend the result numerically to cases where the given assumptions are not satisfied.