Abstract-Sampling-based planners have solved difficult problems in many applications of motion planning in recent years. In particular, techniques based on the Rapidly-exploring Random Trees (RRTs) have generated highly successful singlequery planners. Even though RRTs work well on many problems, they have weaknesses which cause them to explore slowly when the sampling domain is not well adapted to the problem.In this paper we characterize these issues and propose a general framework for minimizing their effect. We develop and implement a simple new planner which shows significant improvement over existing RRT-based planners. In the worst cases, the performance appears to be only slightly worse in comparison to the original RRT, and for many problems it performs orders of magnitude better.

We present methods for efficiently maintaining human head orientation using low-cost MEMS sensors. We particularly address gyroscope integration and compensation of dead reckoning errors using gravity and magnetic fields. Although these problems have been well-studied, our performance criteria are particularly tuned to optimize user experience while tracking head movement in the Oculus Rift Development Kit, which is the most widely used virtual reality headset to date. We also present novel predictive tracking methods that dramatically reduce effective latency (time lag), which further improves the user experience. Experimental results are shown, along with ongoing research on positional tracking.

The problem of generating uniform deterministic samples over the rotation group, SO(3), is fundamental to computational biology, chemistry, physics, and numerous branches of computer science. We present the best-known method to date for constructing incremental, deterministic grids on SO(3); it provides: 1) the lowest metric distortion for grid neighbor edges, 2) optimal dispersionreduction with each additional sample, 3) explicit neighborhood structure, and 4) equivolumetric partition of SO(3) by the grid cells. We also demonstrate the use of the sequence on motion planning problems.

In this paper we analyze the influence of this parameter and propose a new variant of the dynamic-domain RRT, which iteratively adapts the sampling domain for the Voronoi region of each node during the search process. This allows automatic tuning of the parameter and significantly increases the robustness of the algorithm. The resulting variant of the algorithm has been tested on several path planning problems.

The problem of generating uniform deterministic samples over the rotation group, SO(3), is fundamental to computational biology, chemistry, physics, and numerous branches of computer science. We present the best-known method to date for constructing incremental, deterministic grids on SO(3); it provides: 1) the lowest metric distortion for grid neighbor edges, 2) optimal dispersion-reduction with each additional sample, 3) explicit neighborhood structure, and 4) equivolumetric partition of SO(3) by the grid cells. We also demonstrate the use of the sequence on motion planning problems.

The cost of nearest-neighbor (NN) calls is one of the bottlenecks in the performance of sampling-based motion-planning algorithms. Therefore, it is crucial to develop efficient techniques for NN searching in configuration spaces arising in motion planning. In this paper, we present and implement an algorithm for performing NN queries in Cartesian products of , S , and P , the most common topological spaces in the context of motion planning. Our approach extends the algorithm based on kd-trees, called ANN, developed by Arya and Mount for Euclidean spaces. We prove the correctness of the algorithm and illustrate substantial performance improvement over the brute-force approach and several existing NN packages developed for general metric spaces. Our experimental results demonstrate a clear advantage of using the proposed method for both probabilistic roadmaps and rapidly exploring random trees.

Abstruct-This paper addresses the problem of generating uniform deterministic samples over the spheres and the three-dimensional rotation group, SO(3). The target applications include motion planning, optimization, and veriRcation problems in robotics and in related amas, such as graphics, control theory and computational biology. We introduce an infinite sequence of samples that is shown to achieve: 1) low-dispersion, which aids in the development of resolution complete algorithms, 2) lattice structure, which allows easy neighbor identification that is comparable to what is obtained Tor a grid in Wd, and 3) incremental quality, which is similar to that obtained by random sampling. The sequence is demonstrated in a sampling-based motion planning algorithm.

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