Shortest paths synthesis for a car-like robot

Souères, Philippe; Laumond, Jean–Paul

doi:10.1109/9.489204

Cited by 222 publications

(131 citation statements)

References 7 publications

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“…For very few systems, it is possible to compute exactly the locus of goal points reachable by exactly two distinct trajectories (see, for instance, [36] for the case of the car-like robot). This locus is known as the so-called cut-locus in sub-Riemannian geometry.…”

Section: Discussionmentioning

confidence: 99%

An Optimality Principle Governing Human Walking

et al. 2008

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Abstract-In this paper, we investigate different possible strategies underlying the formation of human locomotor trajectories in goal-directed walking. Seven subjects were asked to walk within a motion capture facility from a fixed starting point and direction, and to cross over distant porches for which both position and direction in the room were changed over trials. Stereotyped trajectories were observed in the different subjects. The underlying idea to attack this question has been to relate this problem to an optimal control scheme: the trajectory is chosen according to some optimization principle. This is our basic starting assumption. The subject being viewed as a controlled system, we tried to identify several criteria that could be optimized. Is it the time to perform the trajectory? The length of the path? The minimum jerk along the path?. . . We found that the variation (time derivative) of the curvature of the locomotor paths is minimized. Moreover, we show that the human locomotor trajectories are well approximated by the geodesics of a differential system minimizing the L 2 norm of the control. Such geodesics are made of arcs of clothoids. The clothoid or Cornu spiral is a curve, whose curvature grows with the distance from the origin.

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Section: Discussionmentioning

confidence: 99%

An Optimality Principle Governing Human Walking

et al. 2008

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“…This optimal strategy, although much simpler than the point-to-point time-optimal strategy obtained by P. Souères and J.-P. Laumond in the 1990s (see [45]), is very rich.…”

Section: Introductionmentioning

confidence: 99%

“…The study is done in a reduced state space. On this subject, we have to mention the great work [45] about the more complicated point-to-point problem (see also [1] for a partial study).…”

Section: Introductionmentioning

confidence: 99%

Lyapunov and Minimum-Time Path Planning for Drones

et al. 2014

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In this paper, we study the problem of controlling an unmanned aerial vehicle (UAV) to provide a target supervision and/or to provide convoy protection to ground vehicles.We first present a control strategy based upon a Lyapunov-LaSalle stabilization method to provide supervision of a stationary target. The UAV is expected to join a pre-designed admissible circular trajectory around the target which is itself a fixed point in the space.Our strategy is presented for both HALE (High Altitude Long Endurance) and MALE (Medium Altitude Long Endurance) types UAVs. A UAV flying at a constant altitude (HALE type) is modeled as a Dubins vehicle (i.e. a planar vehicle with constrained turning radius and constant forward velocity). For a UAV that might change its altitude (MALE type), we use the general kinematic model of a rigid body evolving in R 3 . Both control strategies presented are smooth and unlike what is usually proposed in the literature these strategies asymptotically track a circular trajectory of exact minimum turning radius.We also present the time-optimal control synthesis for tracking a circle by a Dubins vehicle. This optimal strategy, although much simpler than the point-to-point time-optimal strategy obtained by P. Souères and J.-P. Laumond in the 1990s (see [45]), is very rich.Finally, we propose control strategies to provide supervision of a moving target, that are based upon the previous ones.

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“…With respect to this metric, the vehicle dynamics are shown to be exponentially stable, opening the way for the establishment of local ISS properties. Similar nonholonomic metrics have been used for characterizing shortest paths [9,10] for mobile robots. A singular perturbation analysis then provides the necessary controller gains that ensure asymptotic stability (exponential in the new metric) for the nominal system and input-to-state stability for the perturbed.…”

Section: Introductionmentioning

confidence: 99%

ISS properties of nonholonomic vehicles

Tanner

2004

Systems & Control Letters

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The paper presents the first result on nonholonomic systems enjoying Input to State Stability (ISS) properties. Although it is known that smooth stabilizability implies ISS, the converse is not generally true. This leaves the possibility of non smoothly stabilizable systems being ISS with respect to a particular input, after an appropriate feedback transformation. This is shown to be true for the case of the unicycle with a dynamic extension, in a particular topology induced by a metric appropriate for this type of systems. A feedback control law renders the closed loop system locally ISS in the particular topology. Potential applications include stability and robustness analysis of formations of mobile robots.

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Shortest paths synthesis for a car-like robot

Cited by 222 publications

References 7 publications

An Optimality Principle Governing Human Walking

An Optimality Principle Governing Human Walking

Lyapunov and Minimum-Time Path Planning for Drones

ISS properties of nonholonomic vehicles

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