Programming and control of robots by means of differential algebraic inequalities

The method of programmed constraints has recently been proposed as an execu table specification language for robot programming. The mathematical struct ures behind such problems are viability problems for control systems descri bed by ordinary differential equations (ODE's) subject to user-defined ineq uality constraints. This paper describes a method for the numerical solutio n of such problems, improving and extending some of our previous results. The algorithm presented is composed of three parts: delay-free discretizati on, local control, and local planning. Delay-free discretizations are consi stent discretizations of control systems described by ODE's with discontinu ous inputs. The local control is based on the minimization of an artificial , logarithmic barrier potential function. Local planning is a computational ly inexpensive way to increase the robustness of the solution procedure, ma king it a refinement to a strategy based on viability alone. Simulations of a mobile robot are used to demonstrate the proposed strategy . Some complementarity is shown between the programmed-constraints approach to robot programming and optimal control, Moreover, we demonstrate the rel ative efficiency of our algorithm compared to optimal control: Typically, o ur method is able to find a solution on the order of 100 times faster than an optimal-control solver.