Motion Planning and Control of Coordinated Systems

Two problems of motion planning for controlled systems which are required to attain a given target set while satisfying coordinated constraints are formulated and solved using dynamic optimization techniques. Constraint coordination arises from the fact that the state of each system is mapped onto state constraints for the other systems. The problems are formulated in terms of backward reach sets which are the sub-zero level sets of appropriate value functions for nonstandard cost functions. The value functions are the solutions of Hamilton-Jacobi-Bellman type PDEs. For linear dynamics and ellipsoidal constraints the value functions are calculated through duality techniques from convex analysis.