Extracting as many possible end configurations as possible

I am trying to implement a path planner to generate a path that moves the robot from q_start to q_goal.

Q_goal is extracted from a stereo camera mounted on the tool, from which I extract x,y,z coordinates of the desired position, the rotation can be arbitrary.

The robot I am using is an industrial ur5 robot arm, the software I use is capable of performing Jacobian based inverse kinematics given a transformation matrix with rotation and translation.

my inverse kinematics provide me with only one solution, which is ok, but doesn't provide me flexibility for path planning...

How do I using inverse kinematics determine all possible q-configurations that fulfills my criteria of having the desired x,y,z coordinates?

• What are the kinematics of your arm? Are you using any kinematics software libraries? (Please expand your question, do not add another comment). – Ben Apr 13 '16 at 13:16
• Hope it provide some form of context to my situation – Carlton Banks Apr 13 '16 at 14:09

Your software library uses a gradient descent method for inverse kinematics. The way this works is that it moves the Cartesian position of the end-effector towards the goal in small steps then gets the joint angles for each step with the relation: $$\Delta \theta= J^{-1}\Delta x$$ This method has a number of nice properties, but as you found you only get one solution.