Programming and control of robots by means of differential algebraic inequalities

|The method of programmed constraints has recently been proposed as an executable speci cation language for robot programming. The mathematical structures behind such problems are viability problems for control systems described by ordinary di erential equations (ODEs) subject to user-de ned inequality constraints. This paper describes a method for the numerical solution of such viability problems, improving and extending results presented in [1]. The algorithm presented is composed of three parts: delay-free discretization, local control, and local planning. Delay-free discretizations are consistent discretizations of control systems described by ODEs with discontinuous inputs. The local control is based on the minimization of an arti cial, logarithmic barrier potential function. Local planning is a computationally inexpensive way to increase the robustness of the solution procedure, making it a re nement to a strategy based on viability alone. Simulations of a mobile robot are used to demonstrate the particular strategy proposed. Some complementarity is shown between the programmed-constraints approach to robot programming and optimal-control approaches. Moreover, we demonstrate the relative e ciency of our algorithm compared to optimal control: Typically, our method is able to nd a solution on the order of one hundred times faster than an optimal-control solver.