Urbanic, R., Hedrick, R., and Djuric, A., "A Linkage Based Solution Approach for Determining 6 Axis Serial Robotic Travel Path Feasibility," SAE Int. J. Mater. Manf. 9(2):444-456, 2016, doi:10.4271/2016-01-0336.
When performing trajectory planning for robotic applications, there are many aspects to consider, such as the reach conditions, joint and end-effector velocities, accelerations and jerk conditions, etc. The reach conditions are dependent on the end-effector orientations and the robot kinematic structure. The reach condition feasibility is the first consideration to be addressed prior to optimizing a solution. The ‘functional’ work space or work window represents a region of feasible reach conditions, and is a sub-set of the work envelope. It is not intuitive to define. Consequently, 2D solution approaches are proposed. The 3D travel paths are decomposed to a 2D representation via radial projections. Forward kinematic representations are employed to define a 2D boundary curve for each desired end effector orientation. The feasible region for all orientations is determined by the use of Boolean intersections of the boundary curves or by overlapping valid regions in which points are placed. Combining the tool path and functional work space regions allow designers to readily visualize regions of concern. A KUKA and Comau robot are used to illustrate the methodology.