An optimal control approach to mode generation in hybrid systems

Mehta, Tejas R.; Egerstedt, Magnus

doi:10.1016/j.na.2005.07.044

Cited by 19 publications

(17 citation statements)

References 30 publications

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“…Inspired by the work in [29], we introduce an interrupt condition ∶ E ↦ {0, 1} , where E is the "energy" in the network, which in turn is a measure of how well the individual task (not the complex mission) is being performed, as was the case in (3) when a negative gradient controller was produced. If E t is the value of E at time t, then the interrupt condition is given by and (E t ) = 0 otherwise.…”

Section: Optimal Behavior Selection Problemsmentioning

confidence: 99%

Sequencing of multi-robot behaviors using reinforcement learning

Pierpaoli

Doan

Romberg

et al. 2021

Control Theory Technol.

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Given a collection of parameterized multi-robot controllers associated with individual behaviors designed for particular tasks, this paper considers the problem of how to sequence and instantiate the behaviors for the purpose of completing a more complex, overarching mission. In addition, uncertainties about the environment or even the mission specifications may require the robots to learn, in a cooperative manner, how best to sequence the behaviors. In this paper, we approach this problem by using reinforcement learning to approximate the solution to the computationally intractable sequencing problem, combined with an online gradient descent approach to selecting the individual behavior parameters, while the transitions among behaviors are triggered automatically when the behaviors have reached a desired performance level relative to a task performance cost. To illustrate the effectiveness of the proposed method, it is implemented on a team of differential-drive robots for solving two different missions, namely, convoy protection and object manipulation.

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Section: Optimal Behavior Selection Problemsmentioning

confidence: 99%

Sequencing of multi-robot behaviors using reinforcement learning

Pierpaoli

Doan

Romberg

et al. 2021

Control Theory Technol.

Self Cite

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“…Examples of alternative methods include the Null Space Methods [35], Navigation Functions [36], and Model Predictive Control [37]. Related to our contribution, solutions to the problem of composing sequences of controllers include formal methods [38], path planning [8], Finite State Machines [39], Petri Nets [40], Behavior Trees [41], and Reinforcement Learning [42], [43]. We take inspiration from a variety of communities in order to develop a unified framework to learn multi-robot controller selection policies from unlabelled and noisy observations of an expert system.…”

Section: A Related Workmentioning

confidence: 99%

Inferring and Learning Multi-Robot Policies by Observing an Expert

Pierpaoli,

Ravichandar,

Waytowich

et al. 2019

Preprint

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In this paper we present a technique for learning how to solve a multi-robot mission that requires interaction with an external environment by repeatedly observing an expert system executing the same mission. We define the expert system as a team of robots equipped with a library of controllers, each designed to solve a specific task, supervised by an expert policy that appropriately selects controllers based on the states of robots and environment. The objective is for an un-trained team of robots equipped with the same library of controllers, but agnostic to the expert policy, to execute the mission, with performances comparable to those of the expert system. From observations of the expert system, the Interactive Multiple Model technique is used to estimate individual controllers executed by the expert policy. Then, the history of estimated controllers and environmental state is used to learn a policy for the un-trained robots. Considering a perimeter protection scenario on a team of simulated differential-drive robots, we show that the learned policy endows the un-trained team with performances comparable to those of the expert system.

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“…Some examples of curves with prescribed length for the Dubins car; see also Figure 3 2) K < 0, locally longest curves: The following constraint holds: F = e 1 cos θ + e 2 sin θ + |e 1 y − e 2 x + e 3 | = K < 0. (25) In this case, the extremal cannot tangentially join ℓ unless it violates the constraint. Hence, either u ≡ 0 or u(t) = sgn(e 1 y(t) − e 2 x(t) + e 3 ) and e 1 cos θ + e 2 sin θ + |e 1 y − e 2 x+e 3 | < 0.…”

Section: B Abnormal Extremalsmentioning

confidence: 99%

“…Conner et al used a set of continuous local feedback control policies and a discrete automaton to plan verifiably correct motions for a mobile robot in a changing environment [14]. Mehta and Egerstedt used optimal control for constructing control programs from a given collection of motion primitives, and also for augmenting the motion primitive set [25]. Frazzoli et al proposed a set of motion primitives, for a six-dimensional aircraft, which contains pieces of optimal trajectories called trim trajectories [18].…”

Section: Introductionmentioning

confidence: 99%

Time-optimal paths for a Dubins airplane

Chitsaz

LaValle

2007

2007 46th IEEE Conference on Decision and Control

203

139

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Abstract-We consider finding a time-optimal trajectory for an airplane from some starting point and orientation to some final point and orientation. Our model extends the Dubins car [15] to have altitude, which leads to Dubins airplane. We assume that the system has independent bounded control over the altitude velocity as well as the turning rate in the plane. Through the use of the Pontryagin Maximum Principle, we characterize the time-optimal trajectories for the system. They are composed of turns with minimum radius, straight line segments, and pieces of planar elastica. One motivation for determining these elementary pieces is for use as motion primitives in modern planning and control algorithms that consider obstacles.

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An optimal control approach to mode generation in hybrid systems

Cited by 19 publications

References 30 publications

Sequencing of multi-robot behaviors using reinforcement learning

Sequencing of multi-robot behaviors using reinforcement learning

Inferring and Learning Multi-Robot Policies by Observing an Expert

Time-optimal paths for a Dubins airplane

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