Michael W. Otte

{\mathrm {RRT^{X}}}: Real-Time Motion Planning/Replanning for Environments with Unpredictable Obstacles

We present \({\mathrm {RRT^{X}}}\), the first asymptotically optimal sampling-based motion planning algorithm for real-time navigation in dynamic environments (containing obstacles that unpredictably appear, disappear, and move). Whenever obstacle changes are observed, e.g., by onboard sensors, a graph rewiring cascade quickly updates the search-graph and repairs its shortest-path -to-goal subtree. Both graph and tree are built directly in the robot’s state space, respect the kinematics of the robot, and continue to improve during navigation. \({\mathrm {RRT^{X}}}\) is also competitive in static environments—where it has the same amortized per iteration runtime as RRT and RRT* \(\varTheta \left( \log {n}\right) \) and is faster than RRT# \(\omega \left( \log ^2{n}\right) \). In order to achieve \(O\left( \log {n}\right) \) iteration time, each node maintains a set of \(O\left( \log {n}\right) \) expected neighbors, and the search graph maintains \(\epsilon \)-consistency for a predefined \(\epsilon \).

Efficient Collision Checking in Sampling-Based Motion Planning

Collision checking is generally considered to be the primary computational bottleneck in sampling-based motion planning algorithms.We show that this does not have to be the case. More specifically, we introduce a novel way of implementing collision checking in the context of sampling-based motion planning, such that the amortized complexity of collision checking is negligible with respect to that of the other components of sampling-based motion planning algorithms. Our method works by storing a lower bound on the distance to the nearest obstacle of each normally collision-checked point. New samples may immediately be determined collision free—without a call to the collision-checking procedure—if they are closer to a previously collision-checked point than the latter is to an obstacle. A similar criterion can also be used to detect points inside of obstacles (i.e., points that are in collision with obstacles). Analysis proves that the expected fraction of points that require a call to the normal (expensive) collision-checking procedure approaches zero as the total number of points increases. Experiments, in which the proposed idea is used in conjunction with the RRT and RRT* path planning algorithms, also validate that our method enables significant benefits in practice.

Local path planning in image space for autonomous robot navigation in unstructured environments

An approach to stereo based local path planning in unstructured environments is presented. The approach differs from previous stereo based and image based planning systems (e.g. top-down occupancy grid planners, autonomous highway driving algorithms, and view-sequenced route representation), in that it uses specialized cost functions to find paths through an occupancy grid representation of the world directly in the image plane and forgoes a projection of cost information from the image plane down onto a top-down 2D Cartesian cost map. We discuss three cost metrics for path selection in image space. We present a basic image based planning system, discuss its susceptibility to rotational and translational oscillation, and present and implement two extensions to the basic system that overcome these limitations - a cylindrical based image system and a hierarchical planning system. All three systems are implemented in an autonomous robot and are tested against a standard top-down 2D Cartesian planning system on three outdoor courses of varying difficulty. We find that the basic image based planning system fails under certain conditions; however, the cylindrical based system is well suited to the task of local path planning and for use as a high resolution local planning component of a hierarchical planning system.

RRTX: Asymptotically optimal single-query sampling-based motion planning with quick replanning

Dynamic environments have obstacles that unpredictably appear, disappear, or move. We present the first sampling-based replanning algorithm that is asymptotically optimal and single-query (designed for situation in which a priori offline computation is unavailable). Our algorithm, RRTX, refines and repairs the same search-graph over the entire duration of navigation (in contrast to previous single-query replanning algorithms that prune and then regrow some or all of the search-tree). Whenever obstacles change and/or the robot moves, a graph rewiring cascade quickly remodels the existing search-graph and repairs its shortest-path-to-goal sub-tree to reflect the new information. Both graph and tree are built directly in the robot’s state-space; thus, the resulting plan(s) respect the kinematics of the robot and continue to improve during navigation. RRTX is probabilistically complete and makes no distinction between local and global planning, yet it reacts quickly enough for real-time high-speed navigation through unpredictably changing environments. Low information transfer time is essential for enabling RRTX to react quickly in dynamic environments; we prove that the information transfer time required to inform a graph of size n about an ε-cost decrease is O(n log n) for RRTX—faster than other current asymptotically optimal single-query algorithms (we prove RRT* is Ω ( n ( n log n ) 1 / D ) and RRT# is ω (n log2 n)). In static environments RRTX has the same amortized runtime as RRT and RRT*, Θ(log n), and is faster than RRT#, ω (log2 n). In order to achieve O(log n) iteration time, each node maintains a set of O(log n) expected neighbors, and the search-graph maintains ε-consistency for a predefined ε. Experiments and simulations confirm our theoretical analysis and demonstrate that RRTX is useful in both static and dynamic environments.

Any-Com Multi-robot Path-Planning: Maximizing Collaboration for Variable Bandwidth

We identify a new class of algorithms for multi-robot problems called “Any-Com” and present the first algorithm belonging to that class: “Any-Com intermediate solution sharing” (or Any-Com ISS) for multi-robot path planning. Any-Com algorithms find a suboptimal solution quickly and then refine that solution subject to communication constraints. This is analogous to the “Any-Time” framework, in which a suboptimal solution is found quickly, and refined as time permits. The current paper focuses on the task of finding a coordinated set of collisionfree paths for all robots in a common area. The computational load of calculating a solution is distributed among all robots, such that the robotic team becomes a distributed computer. Any-Com ISS is probabilistically/resolution complete and a particular robot contributes to the global solution as much as communication reliability permits. Any-Com ISS is “Centralized” in the planning-algorithmic sense that all robots are viewed as pieces of a composite robot; however, there is no dedicated leader and all robots have the same priority. Previous centralized multi-robot navigation algorithms make assumptions about communication topology and bandwidth that are often invalid in the real world. Any-Com allows for collaborative problem solving with graceful performance declines as communication deteriorates. Results are validated experimentally with a team of 5 robots.

Online Learning of Multiple Perceptual Models for Navigation in Unknown Terrain

Autonomous robots in unknown and unstructured environments must be able to distinguish safe and unsafe terrain in order to navigate effectively. Stereo depth data is effective in the near field, but agents should also be able to observe and learn perceptual models for identifying traversable surfaces and obstacles in the far field. As the robot passes through the environment however, the appearance of ground plane and obstacles may vary, for example in open fields versus tree cover or paved versus gravel or dirt tracks. In this paper we describe a working robot navigation system based primarily on colour imaging, which learns sets of fast, efficient density-based models online. As the robot moves through the environment the system chooses whether to apply current models, discard inappropriate models or acquire new ones. These models operate on complex natural images and are acquired and used in real time as the robot navigates.

Any-Com Multi-robot Path-Planning with Dynamic Teams: Multi-robot Coordination under Communication Constraints

We are interested in finding solutions to the multi-robot path-planning problem that have guarantees on completeness, are robust to communication failure, and incorporate varying team size. In this paper we present an algorithm that addresses the complete multi-robot path-planning problem from two different angles. First, dynamic teams are used to minimize computational complexity per robot and maximize communication bandwidth between team-members. Second, each team is formed into a distributed computer that utilizes surplus communication bandwidth to help achieve better solution quality and to speed-up consensus time. The proposed algorithm is evaluated in three real-world experiments that promote dynamic team formation. In the first experiment, a five mobile robot team plans a set of compatible paths through an office environment while communication quality is disrupted using a tin-can Faraday cage. Results show that the distributed framework of the proposed algorithm drastically speeds-up computation, even when packet loss is as high as 97%. In the second and third experiments, four robots are deployed in a network of three building wings connected by a common room. Results of the latter experiments emphasize a need for dynamic team algorithms that can judiciously choose which subset of the original problem a particular dynamic team should solve.

Game theoretic controller synthesis for multi-robot motion planning Part I: Trajectory based algorithms

We consider a class of multi-robot motion planning problems where each robot is associated with multiple objectives and decoupled task specifications. The problems are formulated as an open-loop non-cooperative differential game. A distributed anytime algorithm is proposed to compute a Nash equilibrium of the game. The following properties are proven: (i) the algorithm asymptotically converges to the set of Nash equilibrium; (ii) for scalar cost functionals, the price of stability equals one; (iii) for the worst case, the computational complexity and communication cost are linear in the robot number.

Efficient collision checking in sampling-based motion planning via safety certificates

Collision checking is considered to be the most expensive computational bottleneck in sampling-based motion planning algorithms. We introduce a simple procedure that theoretically eliminates this bottleneck and significantly reduces collision-checking time in practice in several test scenarios. Whenever a point is collision checked in the normal (expensive) way, we store a lower bound on that point’s distance to the nearest obstacle. The latter is called a “safety certificate” and defines a region of the search space that is guaranteed to be collision-free. New points may forgo collision checking whenever they are located within a safety certificate of an old point. Testing the latter condition is accomplished during the nearest-neighbor search that is already part of most sampling-based motion planning algorithms. As more and more points are sampled, safety certificates asymptotically cover the search space and the amortized complexity of (normal, expensive) collision checking becomes negligible with respect to the overall runtime of sampling-based motion planning algorithms. Indeed, the expected fraction of points requiring a normal collision check approaches zero, in the limit, as the total number of points approaches infinity. A number of extensions to the basic idea are presented. Experiments with a number of proof-of-concept implementations demonstrate that using safety certificates can improve the performance of sampling-based motion planning algorithms in practice.

Any-time path-planning: Time-varying wind field + moving obstacles

We consider the problem of real-time path-planning in a spatiotemporally varying wind-field with moving obstacles. We are provided with changing wind and obstacle predictions along a (D + 1)-dimensional space-time lattice. We present an Any-Time algorithm that quickly finds an αβ-suboptimal solution (a path that is not longer than αβ times the optimal time-length), and then improves α and β while planning time remains or until new wind/obstacle predictions trigger a restart. The factor α comes from an α-overestimate of the A*-like cost heuristic. β is proportional to motion modeling error. Any-Time performance is achieved by: (1) improving the connectivity model of the environment from a discrete graph to a continuous cost-field (decreasing β); (2) using the established method of incrementally deflating α. Our method was deployed as the global planner on a fixed-wing unmanned aircraft system that uses Doppler radar and atmospheric models for online real-time wind sensing and prediction. We compare its performance vs. other state-of-the-art methods in simulated environments.