In this paper, we propose a reinforcement learning-based algorithm for trajectory optimization for constrained dynamical systems. This problem is motivated by the fact that for most robotic systems, the dynamics may not always be known. Generating smooth, dynamically feasible trajectories could be difficult for such systems. Using sampling-based algorithms for motion planning may result in trajectories that are prone to undesirable control jumps. However, they can usually provide a good reference trajectory which a model-free reinforcement learning algorithm can then exploit by limiting the search domain and quickly finding a dynamically smooth trajectory. We use this idea to train a reinforcement learning agent to learn a dynamically smooth trajectory in a curriculum learning setting. Furthermore, for generalization, we parameterize the policies with goal locations, so that the agent can be trained for multiple goals simultaneously. We show result in both simulated environments as well as real experiments, for a @math -DoF manipulator arm operated in position-controlled mode to validate the proposed idea. We compare the proposed ideas against a PID controller which is used to track a designed trajectory in configuration space. Our experiments show that our RL agent trained with a reference path outperformed a model-free PID controller of the type commonly used on many robotic platforms for trajectory tracking.
Our combination of RL and reference trajectory tracking can be seen as a form of reward shaping @cite_18 . Reward shaping speeds up learning by creating a more informative reward signal. However, designing shaping rewards requires significant non-trivial reward engineering, and may also alter the optimal solution. To alleviate this problem, automatic reward shaping has been researched @cite_16 @cite_9 .
@cite_9 @cite_18 @cite_16
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This paper investigates the problem of automatically learning how to restructure the reward function of a Markov decision process so as to speed up reinforcement learning. We begin by describing a method that learns a shaped reward function given a set of state and temporal abstractions. Next, we consider decomposition of the per-timestep reward in multieffector problems, in which the overall agent can be decomposed into multiple units that are concurrently carrying out various tasks. We show by example that to find a good reward decomposition, it is often necessary to first shape the rewards appropriately. We then give a function approximation algorithm for solving both problems together. Standard reinforcement learning algorithms can be augmented with our methods, and we show experimentally that in each case, significantly faster learning results. We introduce the use of learned shaping rewards in reinforcement learning tasks, where an agent uses prior experience on a sequence of tasks to learn a portable predictor that estimates intermediate rewards, resulting in accelerated learning in later tasks that are related but distinct. Such agents can be trained on a sequence of relatively easy tasks in order to develop a more informative measure of reward that can be transferred to improve performance on more difficult tasks without requiring a hand coded shaping function. We use a rod positioning task to show that this significantly improves performance even after a very brief training period.