Neural Path Planning: Fixed Time, Near-Optimal Path Generation via Oracle Imitation

Fast and efficient path generation is critical for robots operating in complex environments. This motion planning problem is often performed in a robot's actuation or configuration space, where popular pathfinding methods such as A*, RRT*, get exponentially more computationally expensive to execute as the dimensionality increases or the spaces become more cluttered and complex. On the other hand, if one were to save the entire set of paths connecting all pair of locations in the configuration space a priori, one would run out of memory very quickly. In this work, we introduce a novel way of producing fast and optimal motion plans for static environments by using a stepping neural network approach, called OracleNet. OracleNet uses Recurrent Neural Networks to determine end-to-end trajectories in an iterative manner that implicitly generates optimal motion plans with minimal loss in performance in a compact form. The algorithm is straightforward in implementation while consistently generating near-optimal paths in a single, iterative, end-to-end roll-out. In practice, OracleNet generally has fixed-time execution regardless of the configuration space complexity while outperforming popular pathfinding algorithms in complex environments and higher dimension

Fastron: An Online Learning-Based Model and Active Learning Strategy for Proxy Collision Detection

We introduce the Fastron, a configuration space (C-space) model to be used as a proxy to kinematic-based collision detection. The Fastron allows iterative updates to account for a changing environment through a combination of a novel formulation of the kernel perceptron learning algorithm and an active learning strategy. Our simulations on a 7 degree-of-freedom arm indicate that proxy collision checks may be performed at least 2 times faster than an efficient polyhedral collision checker and at least 8 times faster than an efficient high-precision collision checker. The Fastron model provides conservative collision status predictions by padding C-space obstacles, and proxy collision checking time does not scale poorly as the number of workspace obstacles increases. All results were achieved without GPU acceleration or parallel computing

Collision detection or nearest-neighbor search? On the computational bottleneck in sampling-based motion planning

The complexity of nearest-neighbor search dominates the asymptotic running time of many sampling-based motion-planning algorithms. However, collision detection is often considered to be the computational bottleneck in practice. Examining various asymptotically optimal planning algorithms, we characterize settings, which we call NN-sensitive, in which the practical computational role of nearest-neighbor search is far from being negligible, i.e., the portion of running time taken up by nearest-neighbor search is comparable, or sometimes even greater than the portion of time taken up by collision detection. This reinforces and substantiates the claim that motion-planning algorithms could significantly benefit from efficient and possibly specifically-tailored nearest-neighbor data structures. The asymptotic (near) optimality of these algorithms relies on a prescribed connection radius, defining a ball around a configuration $q$, such that $q$ needs to be connected to all other configurations in that ball. To facilitate our study, we show how to adapt this radius to non-Euclidean spaces, which are prevalent in motion planning. This technical result is of independent interest, as it enables to compare the radial-connection approach with the common alternative, namely, connecting each configuration to its $k$ nearest neighbors ($k$-NN). Indeed, as we demonstrate, there are scenarios where using the radial connection scheme, a solution path of a specific cost is produced ten-fold (and more) faster than with $k$-NN

Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference

We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian process (GP) models. We next develop an efficient gradient-based optimization algorithm that exploits this sparsity and GP interpolation. We call this algorithm the Gaussian Process Motion Planner (GPMP). We then detail how motion planning problems can be formulated as probabilistic inference on a factor graph. This forms the basis for GPMP2, a very efficient algorithm that combines GP representations of trajectories with fast, structure-exploiting inference via numerical optimization. Finally, we extend GPMP2 to an incremental algorithm, iGPMP2, that can efficiently replan when conditions change. We benchmark our algorithms against several sampling-based and trajectory optimization-based motion planning algorithms on planning problems in multiple environments. Our evaluation reveals that GPMP2 is several times faster than previous algorithms while retaining robustness. We also benchmark iGPMP2 on replanning problems, and show that it can find successful solutions in a fraction of the time required by GPMP2 to replan from scratch.Comment: The International Journal of Robotics Research (IJRR), 2018, Volume 37, Issue 1

Learning-Based Proxy Collision Detection for Robot Motion Planning Applications

This paper demonstrates that collision detection-intensive applications such as robotic motion planning may be accelerated by performing collision checks with a machine learning model. We propose Fastron, a learning-based algorithm to model a robot's configuration space to be used as a proxy collision detector in place of standard geometric collision checkers. We demonstrate that leveraging the proxy collision detector results in up to an order of magnitude faster performance in robot simulation and planning than state-of-the-art collision detection libraries. Our results show that Fastron learns a model more than 100 times faster than a competing C-space modeling approach, while also providing theoretical guarantees of learning convergence. Using the OMPL motion planning libraries, we were able to generate initial motion plans across all experiments with varying robot and environment complexities. With Fastron, we can repeatedly perform planning from scratch at a 56 Hz rate, showing its application toward autonomous surgical assistance task in shared environments with human-controlled manipulators. All performance gains were achieved despite using only CPU-based calculations, suggesting further computational gains with a GPU approach that can parallelize tensor algebra. Code is available online

Efficient Penetration Depth Computation between Rigid Models using Contact Space Propagation Sampling

We present a novel method to compute the approximate global penetration depth (PD) between two non-convex geometric models. Our approach consists of two phases: offline precomputation and run-time queries. In the first phase, our formulation uses a novel sampling algorithm to precompute an approximation of the high-dimensional contact space between the pair of models. As compared with prior random sampling algorithms for contact space approximation, our propagation sampling considerably speeds up the precomputation and yields a high quality approximation. At run-time, we perform a nearest-neighbor query and local projection to efficiently compute the translational or generalized PD. We demonstrate the performance of our approach on complex 3D benchmarks with tens or hundreds of thousands of triangles, and we observe significant improvement over previous methods in terms of accuracy, with a modest improvement in the run-time performance.Comment: 10 pages. add the acknowledgemen

Proceedings of the 1st Workshop on Robotics Challenges and Vision (RCV2013)

Proceedings of the 1st Workshop on Robotics Challenges and Vision (RCV2013)Comment: http://compbio.cs.wayne.edu/robotics/rcv2013/proceedings-emb.pd

Online Mapping and Motion Planning under Uncertainty for Safe Navigation in Unknown Environments

Safe autonomous navigation is an essential and challenging problem for robots operating in highly unstructured or completely unknown environments. Under these conditions, not only robotic systems must deal with limited localisation information, but also their manoeuvrability is constrained by their dynamics and often suffer from uncertainty. In order to cope with these constraints, this manuscript proposes an uncertainty-based framework for mapping and planning feasible motions online with probabilistic safety-guarantees. The proposed approach deals with the motion, probabilistic safety, and online computation constraints by: (i) incrementally mapping the surroundings to build an uncertainty-aware representation of the environment, and (ii) iteratively (re)planning trajectories to goal that are kinodynamically feasible and probabilistically safe through a multi-layered sampling-based planner in the belief space. In-depth empirical analyses illustrate some important properties of this approach, namely, (a) the multi-layered planning strategy enables rapid exploration of the high-dimensional belief space while preserving asymptotic optimality and completeness guarantees, and (b) the proposed routine for probabilistic collision checking results in tighter probability bounds in comparison to other uncertainty-aware planners in the literature. Furthermore, real-world in-water experimental evaluation on a non-holonomic torpedo-shaped autonomous underwater vehicle and simulated trials in the Stairwell scenario of the DARPA Subterranean Challenge 2019 on a quadrotor unmanned aerial vehicle demonstrate the efficacy of the method as well as its suitability for systems with limited on-board computational power.Comment: The International Journal of Robotics Research (under review

Group Marching Tree: Sampling-Based Approximately Optimal Motion Planning on GPUs

This paper presents a novel approach, named the Group Marching Tree (GMT*) algorithm, to planning on GPUs at rates amenable to application within control loops, allowing planning in real-world settings via repeated computation of near-optimal plans. GMT*, like the Fast Marching Tree (FMT) algorithm, explores the state space with a "lazy" dynamic programming recursion on a set of samples to grow a tree of near-optimal paths. GMT*, however, alters the approach of FMT with approximate dynamic programming by expanding, in parallel, the group of all active samples with cost below an increasing threshold, rather than only the minimum cost sample. This group approximation enables low-level parallelism over the sample set and removes the need for sequential data structures, while the "lazy" collision checking limits thread divergence---all contributing to a very efficient GPU implementation. While this approach incurs some suboptimality, we prove that GMT* remains asymptotically optimal up to a constant multiplicative factor. We show solutions for complex planning problems under differential constraints can be found in ~10 ms on a desktop GPU and ~30 ms on an embedded GPU, representing a significant speed up over the state of the art, with only small losses in performance. Finally, we present a scenario demonstrating the efficacy of planning within the control loop (~100 Hz) towards operating in dynamic, uncertain settings

Learning the Problem-Optimum Map: Analysis and Application to Global Optimization in Robotics

This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for real-time applications in robotics, since it can produce near-globally optimal solutions orders of magnitude faster than standard methods. This paper establishes theoretical conditions on how many and where samples are needed over the space of problems to achieve a given approximation quality. The framework is applied to solve globally optimal collision-free inverse kinematics (IK) problems, wherein large solution databases are used to produce near-optimal solutions in sub-millisecond time on a standard PC