RMPD - A Recursive Mid-Point Displacement Algorithm for Path Planning

Motivated by what is required for real-time path planning, the paper starts out by presenting sRMPD, a new recursive "local" planner founded on the key notion that, unless made necessary by an obstacle, there must be no deviation from the shortest path between any two points, which would normally be a straight line path in the configuration space. Subsequently, we increase the power of sRMPD by using it as a "connect" subroutine call in a higher-level sampling-based algorithm mRMPD that is inspired by multi-RRT. As a consequence, mRMPD spawns a larger number of space exploring trees in regions of the configuration space that are characterized by a higher density of obstacles. The overall effect is a hybrid tree growing strategy with a trade-off between random exploration as made possible by multi-RRT based logic and immediate exploitation of opportunities to connect two states as made possible by sRMPD. The mRMPD planner can be biased with regard to this trade-off for solving different kinds of planning problems efficiently. Based on the test cases we have run, our experiments show that mRMPD can reduce planning time by up to 80% compared to basic RRT

Bayesian Active Edge Evaluation on Expensive Graphs

Robots operate in environments with varying implicit structure. For instance, a helicopter flying over terrain encounters a very different arrangement of obstacles than a robotic arm manipulating objects on a cluttered table top. State-of-the-art motion planning systems do not exploit this structure, thereby expending valuable planning effort searching for implausible solutions. We are interested in planning algorithms that actively infer the underlying structure of the valid configuration space during planning in order to find solutions with minimal effort. Consider the problem of evaluating edges on a graph to quickly discover collision-free paths. Evaluating edges is expensive, both for robots with complex geometries like robot arms, and for robots with limited onboard computation like UAVs. Until now, this challenge has been addressed via laziness i.e. deferring edge evaluation until absolutely necessary, with the hope that edges turn out to be valid. However, all edges are not alike in value - some have a lot of potentially good paths flowing through them, and some others encode the likelihood of neighbouring edges being valid. This leads to our key insight - instead of passive laziness, we can actively choose edges that reduce the uncertainty about the validity of paths. We show that this is equivalent to the Bayesian active learning paradigm of decision region determination (DRD). However, the DRD problem is not only combinatorially hard, but also requires explicit enumeration of all possible worlds. We propose a novel framework that combines two DRD algorithms, DIRECT and BISECT, to overcome both issues. We show that our approach outperforms several state-of-the-art algorithms on a spectrum of planning problems for mobile robots, manipulators and autonomous helicopters

Asymptotically near-optimal RRT for fast, high-quality, motion planning

We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of 1+epsilon of the optimal solution. Our algorithm allows for a continuous interpolation between the fast RRT algorithm and the asymptotically optimal RRT* and RRG algorithms. When the approximation factor is 1 (i.e., no approximation is allowed), LBT-RRT behaves like RRG. When the approximation factor is unbounded, LBT-RRT behaves like RRT. In between, LBT-RRT is shown to produce paths that have higher quality than RRT would produce and run faster than RRT* would run. This is done by maintaining a tree which is a sub-graph of the RRG roadmap and a second, auxiliary graph, which we call the lower-bound graph. The combination of the two roadmaps, which is faster to maintain than the roadmap maintained by RRT*, efficiently guarantees asymptotic near-optimality. We suggest to use LBT-RRT for high-quality, anytime motion planning. We demonstrate the performance of the algorithm for scenarios ranging from 3 to 12 degrees of freedom and show that even for small approximation factors, the algorithm produces high-quality solutions (comparable to RRG and RRT*) with little running-time overhead when compared to RRT

A Single-Query Manipulation Planner

In manipulation tasks, a robot interacts with movable object(s). The configuration space in manipulation planning is thus the Cartesian product of the configuration space of the robot with those of the movable objects. It is the complex structure of such a "Composite Configuration Space" that makes manipulation planning particularly challenging. Previous works approximate the connectivity of the Composite Configuration Space by means of discretization or by creating random roadmaps. Such approaches involve an extensive pre-processing phase, which furthermore has to be re-done each time the environment changes. In this paper, we propose a high-level Grasp-Placement Table similar to that proposed by Tournassoud et al. (1987), but which does not require any discretization or heavy pre-processing. The table captures the potential connectivity of the Composite Configuration Space while being specific only to the movable object: in particular, it does not require to be re-computed when the environment changes. During the query phase, the table is used to guide a tree-based planner that explores the space systematically. Our simulations and experiments show that the proposed method enables improvements in both running time and trajectory quality as compared to existing approaches.Comment: 8 pages, 7 figures, 1 tabl