Stabilization of trajectories for systems with nonholonomic constraints

Walsh, Greg; Tilbury, Dawn M.; Sastry, S. Shankar; Murray, Richard M.; Laumond, Jean–Paul

doi:10.1109/9.273373

Cited by 228 publications

(81 citation statements)

References 6 publications

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“…In the case of a cart-like mobile robot, solutions to trajectory tracking were introduced in [15] and [16], and a number of improvements have been proposed more recently to relax some of the technical assumptions, e.g., [17], [18], and [19] and/or to cover a broader class of systems, e.g., [20], [21], and [22]. To ensure asymptotic tracking, the controllers in these references require that the reference trajectories sustain ''a degree of activity,'' a property generically referred to as persistence of excitation (PE).…”

Section: Introductionmentioning

confidence: 99%

Obstructions to the Existence of Universal Stabilizers for Smooth Control Systems

Lizárraga

2004

Mathematics of Control, Signals, and Systems (MCSS)

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This paper states necessary conditions for the existence of ''universal stabilizers'' for smooth control systems. Roughly speaking, given a control system and a set U of reference input functions, by ''universal stabilizer'' we mean a continuous feedback law that stabilizes the state of the system asymptotically to any of the reference trajectories produced by (arbitrary) inputs in U. For an example, consider Brockett's nonholonomic integrator, with U representing a set of uniformly bounded, piecewise continuous functions of time. This system's state can be asymptotically stabilized to any reference trajectory provided the latter is persistently exciting (PE). By contrast, for constant trajectories (i.e., equilibria), which are not PE, asymptotic stabilization is impossible by means of continuous pure-state feedback, in view of Brockett's obstruction. However, since this obstruction can be circumvented by the use of time-varying state feedback, one might reasonably expect to be able to design a (time-varying) continuous control law capable of asymptotically stabilizing the state to arbitrary reference trajectories, be they PE or not. Surprisingly, a consequence of the results in this paper is that, for systems with nonholonomic constraints frequently found in control applications, if U contains reference functions that are not PE, then the ''universal stabilization'' problem cannot be solved, even if time-varying feedback is used.

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Section: Introductionmentioning

confidence: 99%

Obstructions to the Existence of Universal Stabilizers for Smooth Control Systems

Lizárraga

2004

Mathematics of Control, Signals, and Systems (MCSS)

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“…However, in the case of underactuated vehicles, that is, when the vehicle has less actuators than state variables to be tracked, the problem is still a very interesting topic of research. Linearization and feedback linearization methods (Walsh et al 1994;Freund and Mayr 1997), as well as Lyapunov-based control laws (Canudas de Wit et al 1993;Fierro and Lewis 1994) have been proposed.…”

Section: Path-followingmentioning

confidence: 99%

A guaranteed obstacle avoidance guidance system

Lapierre

Zapata

2012

Auton Robot

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This paper presents a practical solution to the guidance of a unicycle type robot, including path following, obstacle avoidance and the respect of wheeled actuation saturation constraint, without planning procedure. These results are based on an extension of previous results on path following control including actuation saturation constraints. New solution for obstacle avoidance, with guaranteed performance, is proposed.

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“…As in Laumond et al (1998), the reference point (x, y) is chosen as the mid-point of the rear wheels. A more general model that accounts for the length of the wheelbase is given in Walsh et al (1994). For the sake of simplicity, here we assume that the length of the wheelbase is unity.…”

Section: System Modelmentioning

confidence: 99%

Spatial approaches to broadband jamming in heterogeneous mobile networks: a game-theoretic approach

Bhattacharya

Başar

2011

Auton Robot

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In this paper, we address the problem of a mobile intruder jamming the communication network in a vehicular formation. In order to understand the spatial aspect of the jamming problem, we consider a jamming model that takes into account the relative distance of the jammer from the vehicles. We formulate the problem as a zero-sum pursuitevasion game between a jammer and a team of players with players possessing heterogeneous dynamics. We use Isaacs' approach to arrive at the equations governing the optimal strategies of the team of players. Finally, we obtain the optimal trajectories in the neighborhood of termination by numerically simulating the strategies for some variants of the problem.

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Stabilization of trajectories for systems with nonholonomic constraints

Cited by 228 publications

References 6 publications

Obstructions to the Existence of Universal Stabilizers for Smooth Control Systems

Obstructions to the Existence of Universal Stabilizers for Smooth Control Systems

A guaranteed obstacle avoidance guidance system

Spatial approaches to broadband jamming in heterogeneous mobile networks: a game-theoretic approach

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