An Optimal Control Approach to Flocking

Beaver, Logan E.; Kroninger, Christopher; Malikopoulos, Andreas A.

doi:10.23919/acc45564.2020.9147311

Cited by 10 publications

(13 citation statements)

References 22 publications

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“…where the superscripts − and + correspond to variables evaluated at t − and t + , respectively. Note that µ(t − ) = 0 and g (q) (x(t + ), t + ) = 0, thus those terms do not appear in (13). Substituting ( 11) into ( 13) yields…”

Section: Resultsmentioning

confidence: 99%

“…To solve (31) -( 33) we follow the method outlined in [13]. Since Problem 1 is a generalization of the problem reported in [13], we impose that ||ṙ(t)|| is a constant.…”

Section: B Constrained Motion Primitivementioning

confidence: 99%

“…To solve (31) -( 33) we follow the method outlined in [13]. Since Problem 1 is a generalization of the problem reported in [13], we impose that ||ṙ(t)|| is a constant. This is the reigning optimal solution [17] for this constrained motion primitive.…”

Section: B Constrained Motion Primitivementioning

confidence: 99%

“…Our first contribution has been explored on a case-by-case basis [9]- [11]; however, there has been no general continuity result reported in the literature. Our main result is applicable as a coarse high-level plan for many systems, particularly with applications in connected and automated vehicles [12] and drone swarming [13]. Our barycentric motion constraint is inspired by the distributed formation control law presented in [14].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Energy-Optimal Motion Planning for Agents: Barycentric Motion and Collision Avoidance Constraints

Beaver¹,

Dorothy²,

Kroninger³

et al. 2020

Preprint

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As robotic swarm systems emerge, it is increasingly important to provide strong guarantees on energy consumption and safety to maximize system performance. One approach to achieve these guarantees is through constraint-driven control, where agents seek to minimize energy consumption subject to a set of safety and task constraints. In this paper, we provide a sufficient and necessary condition for an energyminimizing agent with integrator dynamics to have a continuous control input at the transition between unconstrained and constrained trajectories. In addition, we present and analyze barycentric motion and collision avoidance constraints to be used in constraint-driven control of swarms.

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Section: Resultsmentioning

confidence: 99%

“…To solve (31) -( 33) we follow the method outlined in [13]. Since Problem 1 is a generalization of the problem reported in [13], we impose that ||ṙ(t)|| is a constant.…”

Section: B Constrained Motion Primitivementioning

confidence: 99%

Section: B Constrained Motion Primitivementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Energy-Optimal Motion Planning for Agents: Barycentric Motion and Collision Avoidance Constraints

Beaver¹,

Dorothy²,

Kroninger³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We then show that the desired flocking behavior emerges and present some of its properties. The optimal control problem is similar to previous work in constraint driven-flocking [9], [10]. However, in those papers, the authors implemented Reynolds flocking behavior.…”

Section: A Motivationmentioning

confidence: 87%

Beyond Reynolds: A Constraint-Driven Approach to Cluster Flocking

Beaver,

Malikopoulos

2020

Preprint

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In this paper, we present an original set of flocking rules using the ecologically-inspired paradigm for control of multi-robot systems. We translate these rules into a constraintdriven optimal control problem where the agents minimize energy consumption subject to safety and task constraints. We prove several properties about the feasible space of the optimal control problem and show that velocity consensus is an optimal solution. We also motivate the inclusion of slack variables in constraint-driven problems when the global state is only partially observable by each agent. Finally, we present a locally-optimal solution that can be implemented in real time and provide a set of sufficient conditions to guarantee velocity consensus. We validate this control algorithm in simulation.

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An energy-optimal framework for assignment and trajectory generation in teams of autonomous agents

Beaver

Malikopoulos

2020

Systems & Control Letters

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In this paper, we present a decentralized approach to solving the problem of moving N homogeneous agents into N, or more, goal locations along energy-minimizing trajectories. We propose a decentralized framework which only requires knowledge of the goal locations by each agent. The framework includes guarantees on safety through dynamic constraints, and a method to impose a dynamic, global priority ordering on the agents. A solution to the goal assignment and trajectory generation problems are derived in the form of a binary program and a linear system of equations. We also present the conditions for global optimality and characterize the assumptions under which the algorithm is guaranteed to converge to a unique assignment of agents to goals. Finally, we validate the efficacy of our approach through a numerical simulation in MATLAB.

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An Optimal Control Approach to Flocking

Cited by 10 publications

References 22 publications

Energy-Optimal Motion Planning for Agents: Barycentric Motion and Collision Avoidance Constraints

Energy-Optimal Motion Planning for Agents: Barycentric Motion and Collision Avoidance Constraints

Beyond Reynolds: A Constraint-Driven Approach to Cluster Flocking

An energy-optimal framework for assignment and trajectory generation in teams of autonomous agents

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