Module 5 : Trajectory Planning of end effectors
Lecture 12 : Trajectory planning I ( point to point and continuous trajectories)
  Contd...

There are a few issues that come up when we view trajectory planning in the joint space coordinates. Firstly, when individual joints are moved as per the planned trajectory, the links of the robot could physically interfere with each other or the links/end effector could collide with an obstacle in the workspace. Secondly, for a multi-d.o.f. manipulator, the user should not have to specify time histories for each d.o.f. In terms of user interface, therefore, it will be desirable to have a simple way of specifying the task e.g. simply specifying the goal position and orientation of the end-effector and the system should be able to choose appropriate joint motions. Thirdly, since rough and jerky motion could cause vibrations and lead to wear/tear of the system, the joint motions should be “smooth” (i.e. continuity upto say second derivative). Finally, considering manipulator dynamics each joint may have specified upper limits on the acceleration or torque. Thus the trajectory planning problem can be summarized as:

 

Move the manipulator from an initial configuration to final configuration (usually specified in world coordinates rather than joint coordinates) through a sequence of desired intermediate or via-points within the specified duration subject to

Cartesian space path constraints in view of interference and collision with obstacles

Joint space constraints in terms of smoothness of motion and upper limits on acceleration/torque in view of the torque-speed characteristics of the actuator.

 
 

Thus optimal trajectory planning (for example for minimum time) could become quite formidable. Also while we discuss here the details of motion planning, actual motion generation takes place in real time and real world and hence while the robot is operating as a closed loop “motion control” feed back system. Details of control algorithms to achieve the planned motion set points will be discussed separately.

  We will now discuss several simple techniques for trajectory planning in joint space. While we mostly discuss the motion of one joint, the same may be applied to all the joints of the manipulator. For the purpose of discussion, we will consider the case of a revolute joint but the same is applicable to other types of joints also
   
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