Sensor-Based Reactive Navigation in Unknown Convex Sphere Worlds

Abstract

We construct a sensor-based feedback law that provably solves the real-time collision-free robot navigation problem in a compact convex Euclidean subset cluttered with unknown but sufficiently separated and strongly convex obstacles. Our algorithm introduces a novel use of separating hyperplanes for identifying the robot's local obstacle-free convex neighborhood, affording a reactive (online-computed) piecewise smooth and continuous closed-loop vector field whose smooth flow brings almost all configurations in the robot's free space to a designated goal location, with the guarantee of no collisions along the way. We further extend these provable properties to practically motivated limited range sensing models. Disciplines Electrical and Computer Engineering | Engineering | Systems Engineering Comments Note: This paper was nominated for the Best Paper Award at the 12th International Workshop on the Algorithmic Foundations of Robotics in 2016.

Sensor-Based Reactive Execution of Symbolic Rearrangement Plans by a Legged Mobile Manipulator

“…Specifically, we believe this is the first provably correct deliberative/reactive planner to engage an unmodified general purpose mobile manipulator in physical rearrangement of its environment. At the same time, targeting more geometrically realistic environments as well, our new results offer the first formal extension of the recent online, doublyreactive controller family (originated in [16] and extended to our line tracking application in [17]) to nonconvex obstacles. We believe that our "length scale" interpretation of proxregularity [18] used to distinguish suitably "moderate" nonconvexities will also have independent broad future applicability in these settings.…”

“…2) LIDAR Measurement Handling: The LIDAR measurements are pre-processed by the desktop computer before being used by the reactive planner. First of all, following the requirements of [16], range measurements greater than the limit R are set to R. All measurements are projected on the horizontal plane using the robot pitch angle measurement provided by the motion capture system. Finally, when the reactive layer executes a symbolic action MOVETOOBJECT(i, P) or POSITIONOBJECT(i, P), it is critical to recognize the points of the LIDAR pointcloud associated with the object i and not use them for the calculation of the local freespace [1], since i should not be an obstacle.…”

“…1) Anticipated Environment: In the absence of unanticipated obstacles, the robot is in path following mode. Based on the results of [16], [17], this mode is responsible for steering the robot along a reference path P given by the deliberative planner. This is achieved by following the projected-path goal P(α * ) with α * determined as 4 α * := max{α ∈ [0, 1] | P(α) ∈ B (x, d(x, ∂F))} (2) constantly updated as the agent moves along the path.…”

“…In the future, we would like to use the formal guarantees of Theorem 1, whose assumptions are mere sufficient conditions, to extend the application of doubly-reactive planners [16] to nonconvex obstacles in Hilbert spaces.…”

Reactive Semantic Planning in Unexplored Semantic Environments Using Deep Perceptual Feedback

“…N AVIGATION is a fundamentally topological problem [1] reducible to purely reactive (i.e., closed loop state feedback based) solution, given perfect prior knowledge of the environment [2]. For geometrically simple environments, "doubly reactive" methods that reconstruct the local obstacle field on the fly [3], [4], or operate with no need for such reconstruction at all [5], can guarantee collision free convergence to a designated goal with no need for further prior information. However, imperfectly known environments presenting densely cluttered or non-convex obstacles have heretofore required incremental versions of random sampling-based tree construction [6] whose probabilistic completeness can be slow to be realized in practice, especially when confronting settings with narrow passages [7].…”