For motion planning in high dimensional configuration spaces, a significant computational bottleneck is collision detection. Our aim is to reduce the expected number of collision checks by creating a belief model of the configuration space using results from collision tests. We assume the robot's configuration space to be a continuous ambient space whereby neighbouring points tend to share the same collision state. This enables us to formulate a probabilistic model that assigns to unevaluated configurations a belief estimate of being collision-free. We have presented a detailed comparative analysis of various kNN methods and distance metrics used to evaluate C-space belief. We have also proposed a weighting matrix in C-space to improve the performance of kNN methods. Moreover, we have proposed a topological method that exploits the higher order structure of the C-space to generate a belief model. Our results indicate that our proposed topological method outperforms kNN methods by achieving higher model accuracy while being computationally efficient.
For robots with large number of DOFs, planning in configuration space can often be computationally expensive. To speed up the computation, one approach is to split the planning problem into two lower-dimensional sub-problems - planning for the shoulder and elbow joints and that for the wrist joints @cite_12 . Researchers have often projected the configuration space to a lower dimensional space and used topological methods for path planning. @cite_8 shows that under some constraints the topological properties are preserved upon projection.
@cite_12 @cite_8
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Advanced modern humanoid robots often have complex manipulators with a large number of degrees of freedom. Thus, motion planning for such manipulators is a very computationally challenging problem. However, often robotic manipulators allow the wrist degrees of freedom to be controlled independently from the configuration of the rest of the arm. In this paper we show how to split the high dimensional planning problem into two lower-dimensional sub-problems—planning for the main arm joints and planning for the wrist joints, without losing guarantees on completeness. This approach is an extension of our previously developed framework for planning with adaptive dimensionality. Experimentally, we show that this approach is very effective in speeding up planning for robotic arms on Willow Garage’s PR2 platform. We compare our algorithm with several popular alternative approaches for performing motion planning for robotic arms. The results we observe illustrate that our algorithm provides a good balance between planning time, planning success rate, path consistency, and path quality. We present a novel optimization-based motion planning algorithm for high degree-of-freedom (DOF) robots in dynamic environments. Our approach decomposes the high-dimensional motion planning problem into a sequence of low-dimensional sub-problems. We compute collision-free and smooth paths using optimization-based planning and trajectory perturbation for each sub-problem. The overall algorithm does not require a priori knowledge about global motion or trajectories of dynamic obstacles. Rather, we compute a conservative local bound on the position or trajectory of each obstacle over a short time and use the bound to incrementally compute a collision-free trajectory for the robot. The high-DOF robot is treated as a tightly coupled system, and we incrementally use constrained coordination to plan its motion. We highlight the performance of our planner in simulated environments on robots with tens of DOFs.