Control of Nonholonomic Systems

When the generalized velocity of a mechanical system satis es an equality condition that cannot be written as an equivalent condition on the generalized position, the system is called a nonholonomic system [1, 2]. Nonholonomic condition may arise from constraints such as pure rolling of a wheel or from physical conservation laws such as the conservation of angular momentum of a free oating body. Nonholonomic systems pose a particular challenge from the control point of view, as any one who has tried to parallel park a car in a tight space can attest. The basic problem involves nding a path that connects an initial con guration to the nal con guration and satis es all the holonomic and nonholonomic conditions for the system. Both open loop and closed loop solutions are of interest: open loop solution is useful for o -line path generation, closed loop solution is needed for the real time control. Nonholonomic systems typically arise in the following classes of systems: