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I need to get an 8-DOF (degrees of freedom) robot arm to move a specified point. I need to implement the TRPO RL code using OpenAI gym. I already have the gazebo environment. But I am unsure of how to write the code for the reward functions and the algorithm for the joint space motion.

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The most important part of the RL is a reward function. If we want agent to do something specific, we must provide rewards to it in such a way that it will achieve our goals. It is thus very important that the reward function accurately indicates the exact behaviour.

Assume, the robot's goal is to reach desired position as fast as possible. You can construct you reward function so, that it will take into account the Euclidean distance to the position. If the arm moves to the position directly, you will reward the agent with a positive value, otherwise you will punish it with a deviation from the direct line. You probably have other parameters of the joints, such as position and velocity. It can be also included in your reward function, in order to find optimal movements.

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Check out this video from the free udacity overview course on RL and this paper "Setting up a Reinforcement Learning Task with a Real-World Robot"

Here is also related DeepMind's article and paper

I also have a project on github, where I implemented custom Gazebo environment for OpenAI Gym. This allows you to run the test even on a Jupyter Notebook. Check out my example

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