Tasks of the first type are referred to as “Point-to-Point” while the second group of tasks is referred to as “continuous-path” type. In either case, the joints have to be moved such that the end-effector moves through the specified points in the workspace positioning the end-effector at appropriate orientation or passing through those points with desired velocity and/or acceleration within the specified time. Since a robot manipulator tip (i.e. end-effector) carries the tool that performs the desired tasks, it is observed that the end-effector, holding the welding gun, is required to follow a specific path strictly, in order to get a proper weld. The specification of the desired motion naturally occurs in terms of the goal position/orientation of the end-effector in space, its velocity etc. One could visualize a robot system with appropriate sensors that continuously track the global position/orientation etc. of the end-effector and feed these into a closed loop feed-back control system. For such a system, in principle, motion planning, generation and control could take place directly in terms of end-effector's desired motion in world coordinates. However, it must be observed that having to continuously measure the motion variables (such as position, orientation, velocity etc.) of the end-effector in space is not a trivial task. Most manipulators, on the other hand, have individual joint motion sensors that feed into a lower level control system at each joint. Thus we wish to find the individual joint motions required to achieve the desired end-effector motion. A trajectory would thus refer to the time history of position, velocity and acceleration of each individual d.o.f. The individual joint motions and the end-effector motion are of course related through the robot kinematics and can be converted from one to the other.