In this paper we present LQG-MP (linear-quadratic Gaussian motion planning), a new approach to robot motion planning that takes into account the sensors and the controller that will be used during the execution of the robotâs path. LQG-MP is based on the linear-quadratic controller with Gaussian models of uncertainty, and explicitly characterizes in advance (i.e. before execution) the a priori probability distributions of the state of the robot along its path. These distributions can be used to assess the quality of the path, for instance by computing the probability of avoiding collisions. Many methods can be used to generate the required ensemble of candidate paths from which the best path is selected; in this paper we report results using rapidly exploring random trees (RRT). We study the performance of LQG-MP with simulation experiments in three scenarios: (A) a kinodynamic car-like robot, (B) multi-robot planning with differential-drive robots, and (C) a 6-DOF serial manipulator. We also present a method that applies Kalman smoothing to make paths Ck-continuous and apply LQG-MP to precomputed roadmaps using a variant of Dijkstraâs algorithm to efficiently find high-quality paths.

/pdf/lqg-mp-optimized-path-planning-for-robots-with-motion-3x0r2fbpjr.pdf

LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information

We present a differentiable physics engine that can be integrated as a module in deep neural networks for end-to-end learning. As a result, structured physics knowledge can be embedded into larger systems, allowing them, for example, to match observations by performing precise simulations, while achieves high sample efficiency. Specifically, in this paper we demonstrate how to perform backpropagation analytically through a physical simulator defined via a linear complementarity problem. Unlike traditional finite difference methods, such gradients can be computed analytically, which allows for greater flexibility of the engine. Through experiments in diverse domains, we highlight the system's ability to learn physical parameters from data, efficiently match and simulate observed visual behavior, and readily enable control via gradient-based planning methods. Code for the engine and experiments is included with the paper.

/pdf/end-to-end-differentiable-physics-for-learning-and-control-3pzy4b1m7t.pdf

End-to-End Differentiable Physics for Learning and Control

In this paper we address the problem of motion planning for multiple robots. We introduce a prioritized method, based on a powerful method for motion planning in dynamic environments, recently developed by the authors. Our approach is generically applicable: there is no limitation on the number of degrees of freedom of each of the robots, and robots of various types - for instance free-flying robots and articulated robots - can be used simultaneously. Results show that high-quality paths can be produced in less than a second of computation time, even in confined environments involving many robots. We examine three issues in particular in this paper: the assignment of priorities to the robots, the performance of prioritized planning versus coordinated planning, and the influence of the extent by which the robot motions are constrained on the performance of the method. Results are reported in terms of both running time and the quality of the paths produced.

/pdf/prioritized-motion-planning-for-multiple-robots-4zpour96li.pdf

Prioritized motion planning for multiple robots

http://www.roboticsproceedings.org/rss06/p17.pdf

LQG-MP: Optimized Path Planning for Robots with Motion Uncertainty and Imperfect State Information

Many algorithms have been proposed that create a path for a robot in an environment with obstacles. Most methods are aimed at finding a solution. However, for many applications, the path must be of a good quality as well. That is, a path should be short and should keep some amount of minimum clearance to the obstacles. Traveling along such a path reduces the chances of collisions due to the difficulty of measuring and controlling the precise position of the robot. This paper reports a new technique, called Partial shortcut, which decreases the path length. While current methods have difficulties in removing all redundant motions, the technique efficiently removes these motions by interpolating one degree of freedom at a time. Two algorithms are also studied that increase the clearance along paths. The first one is fast but can only deal with rigid, translating bodies. The second algorithm is slower but can handle a broader range of robots, including three-dimensional free-flying and articulated robots, which may reside in arbitrary high-dimensional configuration spaces. A big advantage of these algorithms is that clearance along paths can now be increased efficiently without using complex data structures and algorithms. Finally, we combine the two criteria and show that high-quality paths can be obtained for a broad range of robots.

/pdf/creating-high-quality-paths-for-motion-planning-2xu60f2b9k.pdf

Creating High-quality Paths for Motion Planning

1 Introduction 1.1 Problem Domain 1.2 Historical Background 1.3 Organization 2 Concepts 2.1 Geometry 2.1.1 Notational Conventions 2.1.2 Vector Spaces 2.1.3 Affine Spaces 2.1.4 Euclidean Spaces 2.1.5 Affine Transformations 2.1.6 Three-dimensional Space 2.2 Objects 2.2.1 Polytopes 2.2.2 Polygons 2.2.3 Quadrics 2.2.4 Minkowski Addition 2.2.5 Complex Shapes and Scenes 2.3 Animation 2.4 Time 2.5 Response 2.6 Performance 2.6.1 Frame Coherence 2.6.2 Geometric Coherence 2.6.3 Average Time 2.7 Robustness 2.7.1 Floating-Point Numbers 2.7.2 Stability 2.7.3 Coping with Numerical Problems 3 Basic Primitives 3.1 Spheres 3.1.1 Sphere-Sphere Test 3.1.2 Ray-Sphere Test 3.1.3 Line-Segment-Sphere Test 3.2 Axis-Aligned Boxes 3.2.1 Ray-Box Test 3.2.2 Sphere-Box Test 3.3 Separating Axes 3.3.1 Line-Segment-Box Test 3.3.2 Triangle-Box Test 3.3.3 Box-Box Test 3.4 Polygons 3.4.1 Ray-Triangle Test 3.4.2 Line Segment-Triangle Test 3.4.3 Ray-Polygon Test 3.4.4 Triangle-Triangle Test 3.4.5 Polygon-Polygon Test 3.4.6 Triangle-Sphere Test 3.4.7 Polygon-Volume Tests 4 Convex Objects 4.1 Proximity Queries 4.2 Overview of Algorithms for Polytopes 4.2.1 Finding a Common Point 4.2.2 Finding a Separating Plane 4.2.3 Distance and Penetration Depth Computation 4.3 The Gilbert-Johnson-Keerthi Algorithm 4.3.1 Overview 4.3.2 Convergence and Termination 4.3.3 Johnson's Distance Algorithm 4.3.4 Support Mappings 4.3.5 Implementing the GJK Algorithm 4.3.6 Numerical Aspects of the GJK Algorithm 4.3.7 Testing for Intersections 4.3.8 Penetration Depth 5 Spatial Data Structures 5.1 Nonconvex Polyhedra 5.1.1 Convex Decomposition 5.1.2 Polyhedral Surfaces 5.1.3 Point in Nonconvex Polyhedron 5.2 Space Partitioning 5.2.1 Voxel Grids 5.2.2 Octrees and k-d Trees 5.2.3 Binary Space Partitioning Trees 5.2.4 Discussion 5.3 Model Partitioning 5.3.1 Bounding Volumes 5.3.2 Bounding-Volume Hierarchies 5.3.3 AABB Trees versus OBB Trees 5.3.4 AABB Trees and Deformable Models 5.4 Broad Phase 5.4.1 Sweep and Prune 5.4.2 Implementing the Sweep-and-Prune Algorithm 5.4.3 Ray Casting and AABBs 6 Design of SOLID 6.1 Requirements 6.2 Overview of SOLID 6.3 Design Decisions 6.3.1 Shape Representation 6.3.2 Motion Specification 6.3.3 Response Handling 6.3.4 Algorithms 6.4 Evaluation 6.5 Implementation Notes 6.5.1 Generic Data Types and Algorithms 6.5.2 Fundamental 3D Classes 7 Conclusion 7.1 State of the Art 7.2 Future Work Bibliography Index About the CD-ROM Trademarks

Gino van den Bergen

Papers

Collision Detection in Interactive 3D Environments