Recent advances in laser technology, especially the increase of the cutting speed, has motivated the amendment of the existing robot path methods, which do not allow the complete utilisation of the actuator capabilities and neglect certain particularities in the mechanical design of the wrist of the manipulator arm. This research addresses the optimisation of the six-axis robot motion for continuous contour tracking while considering the redundancy caused by the tool axial symmetry. The particular contribution of the paper is in the area of multi-objective path planning using the graph-based search space representation. In contrast to previous work, the developed optimisation technique is based on dynamic programming and explicitly incorporates verification of the velocity/acceleration constraints. This allows the designer to define interactively their importance with respect to the path-smoothness objectives. In addition, this optimisation technique takes into account the capacity of certain manipulator wrist axes for unlimited rotation in order to produce more economical motion. The efficiency of the developed algorithms has been carefully investigated via computer simulation. The presented results are implemented in a commercial software package and verified for real-life applications in the automotive industry.