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.
@cite_12: 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.
@cite_8: Recent progress in motion planning has made it possible to determine homotopy inequivalent trajectories between an initial and terminal configuration in a robot configuration space. Current approaches have however either assumed the knowledge of differential one-forms related to a skeletonization of the collision space, or have relied on a simplicial representation of the free space. Both of these approaches are currently however not yet practical for higher dimensional configuration spaces. We propose 2D topological task projections (TTPs): mappings from the configuration space to 2-dimensional spaces where simplicial complex filtrations and persistent homology can identify topological properties of the high-dimensional free configuration space. Our approach only requires the availability of collision free samples to identify winding centers that can be used to determine homotopy inequivalent trajectories. We propose the Winding Augmented RRT and RRT* (WA-RRT RRT*) algorithms using which homotopy inequivalent trajectories can be found. We evaluate our approach in experiments with configuration spaces of planar linkages with 2–10 degrees of freedom. Results indicate that our approach can reliably identify suitable topological task projections and our proposed WA-RRT and WA-RRT* algorithms were able to identify a collection of homotopy inequivalent trajectories in each considered configuration space dimension.
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.