When the generalized velo city of a mechanical system satis es an equality condition that cannot b e written as an equivalent condition on the generalized p osition the system is called a nonholonomic system. 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 floating body
Nonholonomic systems p ose a particular challenge from the control p oint of view as any one who has tried to parallel park a car in a tight space can attest The basic problem involves finding a path that connects an initial configuration to the final configuration and satis es all the holonomic and nonholonomic conditions for the system Both op en lo op and closed lo op solutions are of interest open loop solution is useful for online path generation closed loop solution is needed for the real time control
in Control Handbook, Ed. by W. Levine, CRC Press, 1995, pp.1359–1368.