Real-time constrained trajectory generation of mobile manipulators

• A class of non-linear mobile manipulator trajectory generators is proposed.
• The trajectory generation laws are shown to be finite-time stable.
• Collision-free motion generators providing bounded controls are also offered.
• The numerical simulations confirm theoretical results.

This work offers the solution at the control feed-back level of the accurate positioning in a finite time of the end-effector whose mobile manipulator is subject to control and complex state constraints. We propose new forms of various terminal sliding modes (TSM’s) which result from the access to kinematic redundancy of the non-holonomic mechanical system. In order to incorporate control and state inequality constraints into trajectory generation law, both a suitably defined extended task error is introduced and exterior penalty function approach is utilized. In addition, to incorporate holonomic singularity avoidance condition, collision avoidance constraints for the whole mobile manipulator and its final velocity, a suitably defined projection term onto the null space of the extended Jacobian matrix has been introduced. Control limits are maintained by suitable choice of trajectory generator gains. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic differentially steered wheeled mobile platform and a holonomic manipulator of two revolute kinematic pairs, operating both in a two-dimensional unconstrained work space and work space including the obstacles, illustrate performance of the proposed trajectory generators.