Acceleration constraints in modeling and control of nonholonomic systems

Acceleration constraints are used to enhance modeling techniques for dynamical systems. In particular, Kane's equations of motion subjected to bilateral constraints, unilateral constraints, and servo-constraints are modified by utilizing acceleration constraints for the purpose of simplifying the equations and increasing their applicability.; The tangential properties of Kane's method provide relationships between the holonomic and the nonholonomic partial velocities, and hence allow one to describe nonholonomic generalized active and inertia forces in terms of their holonomic counterparts, i.e., those which correspond to the system without constraints. Therefore, based on the modeling process objectives, the holonomic and the nonholonomic vector entities in Kane's approach are used interchangeably to model holonomic and nonholonomic systems. When the holonomic partial velocities are used to model nonholonomic systems, the resulting models are full-order (also called nonminimal or unreduced) and separated in accelerations. As a consequence, they are readily integrable and can be used for generic system analysis. Other related topics are constraint forces, numerical stability of the nonminimal equations of motion, and numerical constraint stabilization.; Two types of unilateral constraints considered are impulsive and friction constraints. Impulsive constraints are modeled by means of a continuous-in-velocities and impulse-momentum approaches.; In controlled motion, the acceleration form of constraints is utilized with the Moore-Penrose generalized inverse of the corresponding constraint matrix to solve for the inverse dynamics of servo-constraints, and for the redundancy resolution of overactuated manipulators. If control variables are involved in the algebraic constraint equations, then these tools are used to modify the controlled equations of motion in order to facilitate control system design. An illustrative example of spacecraft stabilization is presented.