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.