Visual Servoing for Nonholonomically Constrained Three Degree of Freedom Kinematic Systems

Abstract

This paper addresses problems of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case. This is accomplished by switching back and forth between moving "down" and "across" the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, we provide conditions under which the new procedure brings initial configurations to within an arbitrarily small neighborhood of the goal.We summarize simulation results on a sample of visual servoing problems with a few different perceptual models. We document the empirical effectiveness of the proposed algorithm by reporting the results of its application to outdoor autonomous visual registration experiments with the robot RHex guided by engineered beacons. Abstract-This paper addresses problems of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case. This is accomplished by switching back and forth between moving "down" and "across" the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, we provide conditions under which the new procedure brings initial configurations to within an arbitrarily small neighborhood of the goal.We summarize simulation results on a sample of visual servoing problems with a few different perceptual models. We document the empirical effectiveness of the proposed algorithm by reporting the results of its application to outdoor autonomous visual registration experiments with the robot RHex guided by engineered beacons.

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

“…While this approach has been successfully applied in the broad context of visual servoing including the explicit construction of a strict Lyapunov function [10], [21], it is not clear to us how to extend that method to the present setting requiring obstacle avoidance and disturbance rejection in the context of a second-order plant. The alternative of introducing an explicitly nonsmooth (hybrid) point stabilizing law [14] can avoid obstacles but does not extend straightforwardly to second-order dynamics and cannot confer the robustifying ISS properties [16] (i.e., no single strict Lyapunov function can exist) in view of Brockett's condition [22].…”

“…Note that this modification retains the basic task-encoding as well as the convexity properties of the original, while enabling a more faithful reproduction of the γ-defined goal-seeking behavior far from any obstacles. (11), (14) of [7] give rise to relatively more desirable trajectories (metrically) in Z (see Figure 2). Note that we sacrifice the guarantee of convexity ofφ by composing with c −1 , however we conjecture (proof is presently in progress) that the NF properties can be verified without it.…”

“…First, we seek to run the robot over considerably more complex terrain than in [14] and at considerably higher speeds known to necessitate a second-order unicycle model [15] for reasonable fidelity to horizontal plane dynamics. Second, our preoccupation with unstable terrain raises the prospect of significant perturbations, well beyond the infidelities of any unicyle model.…”

Dipole-like fields for stabilization of systems with Pfaffian constraints

“…Since its introduction, the dipolar NF framework has been extended to the motion planning of multiple unicycle-like agents in 2D and 3D environments [28]- [30]. A hybrid control scheme that incorporates the classic NF is proposed in [31] for the navigation of a unicycle-like robot subject to holonomic (sensing) constraints. In [31] the system converges to an arbitrarily small neighborhood of the goal configuration by switching between two distinct vector fields; one that is potential-decreasing and one that is potential-conserving.…”

“…A hybrid control scheme that incorporates the classic NF is proposed in [31] for the navigation of a unicycle-like robot subject to holonomic (sensing) constraints. In [31] the system converges to an arbitrarily small neighborhood of the goal configuration by switching between two distinct vector fields; one that is potential-decreasing and one that is potential-conserving. A harmonic potential field (HPF)-based algorithm for the motion planning of a unicycle-like robot has also been proposed in [32]; this approach is similar in spirit to [27] in the sense of alignment to the field's flow lines, however the unicycle's orientation is not stabilized.…”