Interpolation of a robot joint trajectory is realized using trigonometric splines. This method is based on the assumption that joint-space knots have been generated from cartesian knots by an inverse kinematics algorithm. The use of trigonometric splines results in smooth joint trajectories and is amenable to real-time obstacle avoidance. Some of the spline parameters can be chosen to minimize an objective function (e.g. jerk or energy). If the objective function is minimum jerk, a closed-form solution is obtained. This paper introduces a trajectory interpolation algorithm, discusses a method for trajectory optimization, and includes simulation examples.