# Motion planning with Gaussian Process Regression

I was recently introduced to Gaussian Process Regression (GPR). I read multiple papers regarding use cases of GPR in robotics, however, they were more or less very limited.

Use case from the literature:

• There is a robot arm with 5 joints.
• The authors demonstrate an action such as avoiding an object. After several demonstrations, they build a GPR model.
• Using this trained GPR model, they demonstrate that the robot arm can avoid an object in a similar situation.

Use case that I am wondering:

• I would like to model the basic movements such as move your arm forward but in a certain manner. For example, I would like to train my GPR model so that it can learn the timing when and how long each joint has to move so that this arm can be moved forward in a certain manner that I demonstrated.

• Challenges, in this case, would be that, for instance, the initial joint configuration changes, my trained GPR model will be useless since it is trained for the one specific set of initial joint configuration to move forward.

What could be the solution for this use case? If GPR is not the right choice, what would be the better method?

In the below case, 2 demonstrations are used to represent the behavior/skill. However, in our case, "moving straight forward" action can start from different start posture whereas in the figure below it is always q=0. Now, if we imagine that we are really trying to model this "moving straight forward" more generally (which means for different start postures) the trajectory distribution will be very giant (will probably cover the whole plot).

My question is whether GPR or any regression approach can be used for modeling this kind of general behavior.

skill_avoiding = {