Interpolation of minimum jerk robot joint trajectories through an arbitrary number of knots is realized using a hardwired neural network. The resultant trajectories are numerical rather than analytic functions of time. This application formulates the interpolation problem as a contrained quadratic minimization problem over a continuous joint angle domain and a discrete time domain. Time is discretized according to the robot controller rate. The neuron outputs define the joint angles. An annealing-type method is used to prevent the network from getting stuck in a local minimum. The optimizing neural network and its application to robot path planning are discussed, some simulation results are presented, and the neural network method is compared with other minimum jerk trajectory planning methods