Boundary Tracking and Obstacle Avoidance Using Gyroscopic Control

Zhang, Fumin; Justh, Eric W.; Krishnaprasad, P. S.

doi:10.1007/978-3-0348-0451-6_16

Cited by 7 publications

(23 citation statements)

References 10 publications

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“…But the θ i must also satisfy the closure constraints in (5.8). Substituting (6.23) into the first equation from (5.8), we obtain 24) which holds if and only if (π − ψ + 2 n j=1 α j /n) is one of the n roots of unity, i.e.…”

Section: Remark 62mentioning

confidence: 99%

Symmetry and reduction in collectives: cyclic pursuit strategies

2013

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We specify and analyse models that capture the geometry of purposeful motion of a collective of mobile agents, with a focus on planar motion, dyadic strategies and attention graphs which are static, directed and cyclic. Strategies are formulated as constraints on joint shape space and are implemented through feedback laws for the actions of individual agents, here modelled as self-steering particles. By reduction to a labelled shape space (using a redundant parametrization to account for cycle closure constraints) and a further reduction through time rescaling, we characterize various special solutions (relative equilibria and pure shape equilibria) for cyclic pursuit with a constant bearing (CB) strategy. This is accomplished by first proving convergence of the (nonlinear) dynamics to an invariant manifold (the CB pursuit manifold), and then analysing the closedloop dynamics restricted to the invariant manifold. For illustration, we sketch some low-dimensional examples. This formulation-involving strategies, attention graphs and sensor-driven steering lawsand the resulting templates of collective motion, are part of a broader programme to interpret the mechanisms underlying biological collective motion.

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Section: Remark 62mentioning

confidence: 99%

Symmetry and reduction in collectives: cyclic pursuit strategies

2013

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“…It follows from Theorem 3 that H 1 (ρ * 1 ,ζ, K 1 ) × H 2 (ρ * 2 ,θ, K 2 ) is robustly forward invariant for (40) for all disturbances (δ 1 ,δ 2 ) for which the right side of (42) is below δ * i for i = 1, 2. We have therefore shown the following.…”

Section: Robust Forward Invariance Under Input Delaysmentioning

confidence: 90%

“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php (40) is the special case of (39) with (δ 1 (t), δ 2 (t)) = (Ξ ζ (Y t ) +δ 1 (t), Ξ θ (Y t ) +δ 2 (t)), which satisfy…”

Section: Robust Forward Invariance Under Input Delaysmentioning

confidence: 99%

“…is robustly forward invariant for the adaptive delayed curve tracking dynamics (40) for all disturbances…”

Section: Robust Forward Invariance Under Input Delaysmentioning

confidence: 99%

“…Let r 2 denote the position of the free particle moving at unit speed, x 2 the unit tangent vector to the trajectory of its moving center, y 2 a corresponding unit normal vector, and z 2 = x 2 × y 2 . With the speed defined by ds dt = α, the time evolutions of the free point and the closest point on the curve are given by [40]:…”

Section: Modelmentioning

confidence: 99%

See 2 more Smart Citations

Robustness of Adaptive Control under Time Delays for Three-Dimensional Curve Tracking

Malisoff¹,

Zhang²

2015

SIAM J. Control Optim.

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We analyze the robustness of a class of controllers that enable three-dimensional curve tracking by a free moving particle. The free particle tracks the closest point on the curve. By building a strict Lyapunov function and robustly forward invariant sets, we show input-to-state stability under predictable tolerance and safety bounds that guarantee robustness under control uncertainty, input delays, and a class of polygonal state constraints, including adaptive tracking and parameter identification under unknown control gains. Such an understanding may provide certified performance when the control laws are applied to real-life systems. Introduction.Curve tracking is a central problem in control and path planning for mobile robots [1,8,27,36,37]. The work presented in [39] used a nonstrict Lyapunov function to find feedback controllers that ensure that a robot moves parallel to a two-dimensional (2D) curve. See also [32] for chained form systems that capture the nonholonomic dynamics of a large variety of mobile robots, such as a kinematic car with trailers, which led to extended curve tracking control laws, and [12] for a reformulation of 2D curve tracking in the three-dimensional (3D) case. Curve tracking is also important for cooperative controllers that track motion for multiple mobile robots; see [38] for applications to ocean sensing. The controls in the works cited above have been found to give reliable performance, even under severe perturbations, in farming [18], obstacle avoidance in corridors [41], and ocean sampling [38].Given a curve tracking control, we are interested in deriving predictable safety and tolerance bounds under several types of uncertainty and input delays, and in identifying unknown control gains. To this end, this paper presents novel 3D analogs of the robustness results that we derived for 2D in [20,21]. For 2D tracking, [20] proved robustness using input-to-state stability (ISS) with respect to actuator errors and robust forward invariance, which gave predictable tolerance and safety bounds under time delays and a class of polygonal state constraints. Briefly described, robust forward invariance means forward invariance in the usual sense of differential equations, but that is also preserved under perturbations; see section 3 for the precise definition. Actuator errors can be modeled as additive perturbations on controls, and communication delays are also common [6, 16], e.g., in marine robotics where there may only be intermittent communications under unfriendly sea conditions. In

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Robustness of a class of three-dimensional curve tracking control laws under time delays and polygonal state constraints

Malisoff

Zhang

2013

2013 American Control Conference

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We analyze the robustness of a class of controllers that enable three-dimensional curve tracking of free moving particles. By building a strict Lyapunov function and robustly forwardly invariant sets, we show input-to-state stability under predictable tolerance and safety bounds that guarantee robustness under control uncertainty, input delays, and a class of polygonal state constraints. Such understanding may provide certified performance when the control laws are applied to real life systems. We demonstrate our findings in simulations.

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Boundary Tracking and Obstacle Avoidance Using Gyroscopic Control

Cited by 7 publications

References 10 publications

Symmetry and reduction in collectives: cyclic pursuit strategies

Symmetry and reduction in collectives: cyclic pursuit strategies

Robustness of Adaptive Control under Time Delays for Three-Dimensional Curve Tracking

Robustness of a class of three-dimensional curve tracking control laws under time delays and polygonal state constraints

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