Joint Manifolds and Markov Decision Process in Robot Motion Planning

Learning trajectories for a robot in unknown environments which can be generalized to different types of robots is a challenging problem. The input space is very high dimensional and any type of algorithm and computation has a very high time complexity and challenging to define problems in such a high state space. Applying low-dimensional reduction to such problems does the trick for us. We can reduce the high dimensional input data to a low dimensional represenatation and use it to learn and plan paths for a robot. 1. Problem Statement and Idea In this work, we plan to learn trajectories for a robot, avoiding obstacles and reaching a certain goal keeping the robot constraints like the physical joint constraints and avoidance of occulusions. We expect sample images of various robot’s positions available to us and too from various cameras. We intend to use joint manifold kind of structure to learn the robot’s structure and surroundings. Path planning can be then generalized to unknown environments and unknown obstacles.The idea is that markov Decision processes can also be used to solve robot path planning problem using various poses as states and defining valid transitions dedpending upon the constraints. The problem of path planning is intricate due to high dimensional input space. The images are obtained continuously from the cameras, which contribute to large amount of data and that too on a very high dimenisional space. The computations on this high dimensional space are very complex and take ample time to do any trivial computations on such a space. To solve such problems , we need a mapping function that will map such highdimensional data to a low dimensional space. The mapping can be linear or non-linear depending upon the intrinsic manifold structure. The lowdimensional construction of robot’s sensorymotor state space will lead to ease of planning and computations and representations.