Dynamical trajectory replanning for uncertain environments

Abstract

We propose a dynamical reference generator equipped with an augmented transient "replanning" subsystem that modulates a feedback controller's efforts to force a mechanical plant to track the reference signal. The replanner alters the reference generator's output in the face of unanticipated disturbances that drive up the tracking error. We demonstrate that the new reference generator cannot destabilize the tracker, that tracking errors converge in the absence of disturbance, and that the overall coupled reference-tracker system cannot be destabilized by disturbances of bounded energy. We report the results of simulation studies exploring the performance of this new design applied to a two dimensional point mass particle interacting with fixed but unknown terrain obstacles. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/644 Dynamical Trajectory Replanning for Uncertain EnvironmentsShai Revzen* B. Denizİlhan* Daniel E. Koditschek* Abstract-We propose a dynamical reference generator equipped with an augmented transient "replanning" subsystem that modulates a feedback controller's efforts to force a mechanical plant to track the reference signal. The replanner alters the reference generator's output in the face of unanticipated disturbances that drive up the tracking error. We demonstrate that the new reference generator cannot destabilize the tracker, that tracking errors converge in the absence of disturbance, and that the overall coupled reference-tracker system cannot be destabilized by disturbances of bounded energy. We report the results of simulation studies exploring the performance of this new design applied to a two dimensional point mass particle interacting with fixed but unknown terrain obstacles.

Autonomous legged hill ascent

“…where p h = [0, 10] T denotes the only critical point of the hill which is stable. This construction is similar to the saturation term in (Revzen et al, 2012), which results in a gradient vector with bounded magnitude, Γ h = √ 2, and a positive-definite Hessian with bounded curvatures, κ φ = 1/ξ = 1. Let us introduce a single obstacle located at the origin, p c = 0, resulting in the minimum task gradient magnitude over the obstacle region, Ω h = 1.…”

A drift-diffusion model for robotic obstacle avoidance

“…Rather, we posit that the modified navigation function controller [7] implemented in these experiments introduces local deterministic interactions with obstacles that would be better modeled by the case of a plastic collision -i.e., the case = 0 in Section II-A, Assumption 4. Looking ahead to assessing the efficacy of more sophisticated local replanners [7], we are pursuing the analysis of the more general "scattering" collision models discussed in that section. However, these more sophisticated analyses all lie beyond the scope of the present paper.…”

“…Recent efforts to confer on these dynamically effective, formally correct but undeservedly optimistic methods [2], [5] a formalizable degree of robustness against such uncertainties have yielded an approach to dynamical replanning [7] that introduces an internal model capable of inferring and reacting to the presence of an unexpected obstacle by exciting special behaviors that promote escape. Unfortunately, the problem representation suitable to sound reasoning about the dynamical implications of these methods leaves a substantial gap with respect to the implications relating to knowledge about the geometric properties of the environment-most crucially, the obstacle loci and shape.…”

“…For now, as a first step toward a stochasticallyenhanced version of the deterministic replanner [7], we simply replace it and introduce stochastic noise into the otherwise deterministic robot dynamics and reason about the statistics of the resulting interaction with the uncertain local geometric environment. Unsurprisingly, this approach allows a more natural representation of that uncertainty.…”

Active sensing for dynamic, non-holonomic, robust visual servoing

“…Fully-actuated first-order visual servo control is largely a solved problem [1] and, in particular, smooth stabilizability opens the door to the full suite of navigation function (NF) methods [7], including the lift to second-order dynamics [17] that can preserve all the first-order guarantees-not merely convergence, but obstacle avoidance [18], and robustness against disturbances as well [19]. Recent work incorporating visual servo methods into global landmark-based localization, navigation and mapping [20], [21] suggests the powerful role that effectively stabilized visual servo loops can achieve in complex task settings.…”