Recent advances in laser technology, and especially essential increase of the cutting speed, motivate amendment of the existing robot path methods, which do not allow complete utilisation of the actuator capabilities and also neglect some particularities in the mechanical design of the manipulator arm wrist. This research addresses the optimisation of the 6-axes robot motions for the continuous contour tracking taking into account 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. The developed path planning algorithm is based on the dynamic programming, which incorporates the constraint checking for each segment of a candidate solution and the penalty assignment for the constraint violation. To generate the smooth motion, each joint trajectory is evaluated by a set of performance indices such as the coordinate deviation, maximum increment, and total displacement of the axes. During the optimisation, the vector objective is converted into the scalar one using the weighted sum or minimax criterion, while the distance between the successive tool locations is evaluated using three types of the distance metrics. In contrast to the previous works, the developed optimisation technique explicitly incorporates verification of the velocity/acceleration constrains, allowing the designer interactively define their importance with respect to the path-smoothness objectives. In addition, it takes into account the capacity of some manipulator wrist axes for unlimited rotation in order to produce more economical motions. 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 automotive industry.