TechTalks from event: Technical session talks from ICRA 2012

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Motion Path Planning I

  • Navigation Functions for Everywhere Partially Sufficiently Curved Worlds Authors: Filippidis, Ioannis; Kyriakopoulos, Kostas
    We extend Navigation Functions (NF) to worlds of more general geometry and topology. This is achieved without the need for diffeomorphisms, by direct definition in the geometrically complicated configuration space. Every obstacle boundary point should be partially sufficiently curved. This requires that at least one principal normal curvature be sufficient. A normal curvature is termed sufficient when the tangent sphere with diameter the associated curvature radius is a subset of the obstacle. Examples include ellipses with bounded eccentricity, tori, cylinders, one-sheet hyperboloids and others. Our proof establishes the existence of appropriate tuning for this purpose. Direct application to geometrically complicated cases is illustrated through nontrivial simulations.
  • Trajectory Tracking among Landmarks and Binary Sensor-Beams Authors: Tovar, Benjamin; Murphey, Todd
    We study a trajectory tracking problem for a mobile robot moving in the plane using combinatorial observations from the state. These combinatorial observations come from crossing binary detection beams. A binary detection beam is a sensing abstraction arising from physical sensor beams or virtual beams that are derived from several sensing modalities, such as actual detection beams in the environment, changes in the angular order of landmarks around the robot, or recognizable markings in the plane. We solve the filtering problem from a geometric perspective and present its relation to linear recursive filters in control theory. Subsequently, we develop the acceleration control of the robot to track a given input trajectory, with a finite control set consisting on moving toward landmarks naturally modeling the robot as a switched dynamical system. We present experiments using an e-puck differential-drive robot, in which a useful estimate of the state for tracking is produced regardless of nontrivial uncertainty.
  • A Singularity-Free Path Planner for Closed-Chain Manipulators Authors: Bohigas, Oriol; Henderson, Michael E.; Ros, Lluis; Porta, Josep M
    This paper provides an algorithm for computing singularity-free paths on non-redundant closed-chain manipulators. Given two non-singular configurations of the manipulator, the method attempts to connect them through a configuration space path that maintains a minimum clearance with respect to the singularity locus at all points. The method is resolution-complete, in the sense that it always returns a path if one exists at a given resolution, or returns "failure'' otherwise. The path is computed by defining a new manifold that maintains a one-to-one correspondence with the singularity-free configuration space of the manipulator, and then using a higher-dimensional continuation technique to explore this manifold systematically from one configuration, until the second configuration is found. Examples are included that demonstrate the performance of the method on illustrative situations.
  • Comparison of Constrained Geometric Approximation Strategies for Planar Information States Authors: Song, Yang; O'Kane, Jason
    This paper describes and analyzes a new technique for reasoning about uncertainty called constrained geometric approximation (CGA). We build upon recent work that has developed methods to explicitly represent a robot's knowledge as an element, called an information state, in an appropriately defined information space. The intuition of our new approach is to constrain the I-state to remain in a structured subset of the I-space, and to enforce that constraint using appropriate overapproximation methods. The result is a collection of algorithms that enable mobile robots with extreme limitations in both sensing and computation to maintain simple but provably meaningful representations of the incomplete information available to them. We present a simulated implementation of this technique for a sensor-based navigation task, along with experimental results for this task showing that CGA, compared to a high-fidelity representation of the un-approximated I-state, achieves a similar success rate at a small fraction of the computational cost.
  • Voxel-Based Motion Bounding and Workspace Estimation for Robotic Manipulators Authors: Anderson-Sprecher, Peter; Simmons, Reid
    Identification of regions in space that a robotic manipulator can reach in a given amount of time is important for many applications, such as safety monitoring of industrial manipulators and trajectory and task planning. However, due to the high-dimensional configuration space of many robots, reasoning about possible physical motion is often intractable. In this paper, we propose a novel method for creating a <i>reachability grid</i>, a voxel-based representation that estimates the minimum time needed for a manipulator to reach any physical location within its workspace. We use up to second-degree constraints on joint motion to model motion limits for each joint independently, followed by successive voxel approximations to map these limits on to the robot’s physical workspace. Results using a simulated manipulator indicate that our method can produce accurate reachability grids in real-time, even for robots with many degrees of freedom. Furthermore, errors are almost exclusively biased towards producing more optimistic reachability estimates, which is a desirable characteristic for many applications.
  • Branch and Bound for Informative Path Planning Authors: Binney, Jonathan; Sukhatme, Gaurav
    We present an optimal algorithm for informative path planning (IPP), using a branch and bound method inspired by feature selection algorithms. The algorithm uses the monotonicity of the objective function to give an objective function-dependent speedup versus brute force search. We present results which suggest that when maximizing variance reduction in a Gaussian process model, the speedup is significant.