Goal Directed Design of Manipulators Based on Task Descriptions

Sarosh Patel
Tarek Sobh

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Inverse Kinematics Using Particle Swarm Optimization

   A two degree of freedom planar manipulator has a maximum of two inverse solutions for all points except when the arm is fully extended. These two are commonly referred to as 'elbow up' and 'elbow down' postures, as shown in the figure below:

   

 The figure below shows the contour plot of the error function and the location of the two solutions. The two minima points are the required inverse kinematic solutions.



The video below shows how the two inverse kinematic solutions are found using particle swarm optimization.


For a high degree of freedom manipulator such as a Puma560 there are four positional inverse kinematic solutions. These can also be found using PSO by decoupling the positioning and orienting joints. Also the PSO algorithm can limit the search space such that only solutions within the specified joint constraints are found. Below video shows the four position and orientation solution found for a Puma560 manipulator using the PSO algorithm.