Controllability of Mechanical Systems under Account of Phase Constraints

The problem of controllability of mechanical systems is investigated. The specific features are connected with the account of phase constraints imposed on the system. It is necessary to find out whether there exists a controllability domain, the domain where the motion trajectory of the system can start and finish. Note that these motions have to lie in a domain given by phase constraints. The constraints may reflect, e.g., design conditions, requirements, etc. Say, as applied to a manipulator, these conditions can determine an interval of admissible angular positions of its links. Conditions are found when there exists a nonempty controllability domain for given phase constraints. These conditions have an obvious physical meaning. The conditions are connected with the domination of control forces over other generalized forces (weight forces, resistance forces of the external environment, etc.). The domination is necessary in the rate of force variation (i.e., the derivative). In other words, it is required that the control actuators of the mechanical system admit sufficiently fast variation of the output control signal. The controllability conditions are similar to the conditions obtained in [1-7], where mechanical systems without constraints were investigated.