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Path planning and re-planning for serial 6 degree of freedom (DOF) robotic systems is challenging due to complex kinematic structure and application conditions which affects the robot's tool frame position, orientation and singularity avoidance. These three characteristics represent the key elements for production planning and layout design of the automated manufacturing systems. The robot trajectory represents series of connected points in 3D space. Each point is defined with its position and orientation related to the robot's base frames or predefined user frame. The robot will move from point to point using the desired motion type (linear, arc, or joint). The trajectory planning requires first to check if robot can reach the selected part(s). This can be simply done by placing the part(s) inside the robot's work envelope. The robot's work envelope represents a set of all robots' reachable points without considering their orientation.

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.