A method of planning collision-free trajectory for a mobile manipulator tracking a line section path is presented. The reference trajectory of a mobile platform is not needed, mechanical and control constraints are taken into account. The method is based on a penalty function approach and a redundancy resolution at the acceleration level. Nonholonomic constraints in a Pfaffian form are explicitly incorporated to the control algorithm. The problem is shown to be equivalent to some point-to-point control problem whose solution may be easier determined. The motion of the mobile manipulator is planned in order to maximise the manipulability measure, thus to avoid manipulator singularities. A computer example involving a mobile manipulator consisting of a nonholonomic platform (2,0) class and a 3 DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.
This paper presents control method for multiple two-wheeled mobile robots moving in formation. Trajectory tracking algorithm from [7] is extended by collision avoidance, and is applied to the different type of formation task: each robot in the formation mimics motion of the virtual leader with a certain displacement. Each robot avoids collisions with other robots and circular shaped, static obstacles existing in the environment. Artificial potential functions are used to generate repulsive component of the control. Stability analysis of the closed-loop system is based on Lyapunov-like function. Effectiveness of the proposed algorithm is illustrated by simulation results.