Curved path approaches and dynamic interpolation

It is shown that to simplify the specification of a desired trajectory for some subset of the variables of a dynamic control system, it may be advantageous to designate a set of intercept points that the trajectory is required to pass through. The system controls can then be computed in terms of a spline function to meet these requirements for dynamic interpolation. Optimization of a cost function under continuity constraints can be imbedded in the determination of spline coefficients to obtain certain desirable geometric properties of the resulting trajectory. The optimal trajectories determined under the additional constraint of constant speed are useful in determining the acceptability of the results of dynamic interpolation