This paper describes Motion Planning Networks (MPNet), a computationally efficient, learning-based neural planner for solving motion planning problems. MPNet uses neural networks to learn general near-optimal heuristics for path planning in seen and unseen environments. It receives environment information as point-clouds, as well as a robot's initial and desired goal configurations and recursively calls itself to bidirectionally generate connectable paths. In addition to finding directly connectable and near-optimal paths in a single pass, we show that worst-case theoretical guarantees can be proven if we merge this neural network strategy with classical sample-based planners in a hybrid approach while still retaining significant computational and optimality improvements. To learn the MPNet models, we present an active continual learning approach that enables MPNet to learn from streaming data and actively ask for expert demonstrations when needed, drastically reducing data for training. We validate MPNet against gold-standard and state-of-the-art planning methods in a variety of problems from 2D to 7D robot configuration spaces in challenging and cluttered environments, with results showing significant and consistently stronger performance metrics, and motivating neural planning in general as a modern strategy for solving motion planning problems efficiently.
Biased sampling heuristics adaptively sample the robot state-space to overcome limitations caused by random uniform exploration in underlying SMP methods. For instance, P-RRT* @cite_15 @cite_61 incorporates artificial potential fields @cite_42 into RRT* to generate goal directed trees for rapid convergence to an optimal path solution. In similar vein, proposed the Informed-RRT* @cite_33 and BIT* (Batch Informed Trees) @cite_13 . Informed-RRT* defines an ellipsoidal region using RRT*'s initial path solution to adaptively sample the configuration space for optimal path planning. Despite improvements in computation time, Informed-RRT* suffers in situations where finding an initial path is itself challenging. On the other hand, BIT* is an incremental graph search method that instantiates a dynamically-changing ellipsoidal region for batch sampling to compute paths. Despite some improvements in computation speed, these biased sampling heuristics still suffer from the curse of dimensionality.
@cite_61 @cite_33 @cite_42 @cite_15 @cite_13
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Abstract The sampling-based motion planning algorithm known as Rapidly-exploring Random Trees (RRT) has gained the attention of many researchers due to their computational efficiency and effectiveness. Recently, a variant of RRT called RRT* has been proposed that ensures asymptotic optimality. Subsequently its bidirectional version has also been introduced in the literature known as Bidirectional-RRT* (B-RRT*). We introduce a new variant called Intelligent Bidirectional-RRT* (IB-RRT*) which is an improved variant of the optimal RRT* and bidirectional version of RRT* (B-RRT*) algorithms and is specially designed for complex cluttered environments. IB-RRT* utilizes the bidirectional trees approach and introduces intelligent sample insertion heuristic for fast convergence to the optimal path solution using uniform sampling heuristics. The proposed algorithm is evaluated theoretically and experimental results are presented that compares IB-RRT* with RRT* and B-RRT*. Moreover, experimental results demonstrate the superior efficiency of IB-RRT* in comparison with RRT* and B-RRT in complex cluttered environments. Rapidly-exploring random trees (RRTs) are pop- ular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sam- pled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on complete- ness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show exper- imentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem. During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms, e.g., in terms of a given cost function, have been established so far. The purpose of this paper is to fill this gap, by designing efficient incremental samplingbased algorithms with provable optimality properties. The first contribution of this paper is a negative result: it is proven that, under mild technical conditions, the cost of the best path returned by RRT converges almost surely to a non-optimal value, as the number of samples increases. Second, a new algorithm is considered, called the Rapidly-exploring Random Graph (RRG), and it is shown that the cost of the best path returned by RRG converges to the optimum almost surely. Third, a tree version of RRG is introduced, called RRT∗, which preserves the asymptotic optimality of RRG while maintaining a tree structure like RRT. The analysis of the new algorithms hinges on novel connections between sampling-based motion planning algorithms and the theory of random geometric graphs. In terms of computational complexity, it is shown that the number of simple operations required by both the RRG and RRT∗ algorithms is asymptotically within a constant factor of that required by RRT. In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm FMT*. The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art counterparts, chiefly PRM* and RRT*. The FMT* algorithm performs a 'lazy' dynamic programming recursion on a predetermined number of probabilistically drawn samples to grow a tree of paths, which moves steadily outward in cost-to-arrive space. As such, this algorithm combines features of both single-query algorithms chiefly RRT and multiple-query algorithms chiefly PRM, and is reminiscent of the Fast Marching Method for the solution of Eikonal equations. As a departure from previous analysis approaches that are based on the notion of almost sure convergence, the FMT* algorithm is analyzed under the notion of convergence in probability: the extra mathematical flexibility of this approach allows for convergence rate bounds-the first in the field of optimal sampling-based motion planning. Specifically, for a certain selection of tuning parameters and configuration spaces, we obtain a convergence rate bound of order On −1 d+? , where n is the number of sampled points, d is the dimension of the configuration space, and ? is an arbitrarily small constant. We go on to demonstrate asymptotic optimality for a number of variations on FMT*, namely when the configuration space is sampled non-uniformly, when the cost is not arc length, and when connections are made based on the number of nearest neighbors instead of a fixed connection radius. Numerical experiments over a range of dimensions and obstacle configurations confirm our theoretical and heuristic arguments by showing that FMT*, for a given execution time, returns substantially better solutions than either PRM* or RRT*, especially in high-dimensional configuration spaces and in scenarios where collision-checking is expensive.