A Level Set Approach to Online Sensing and Trajectory Optimization with Time Delays

Kirchner, Matthew R.

doi:10.1016/j.ifacol.2019.08.087

Cited by 7 publications

(3 citation statements)

References 18 publications

(26 reference statements)

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“…The Hamilton-Jacobi formulation presented has other advantages for multi-robot systems, such as the compensation of time delays which can be induced in several ways including computation, sensing, and inter-robot communication. See for example [41].…”

Section: Discussionmentioning

confidence: 99%

A Hamilton-Jacobi Formulation for Optimal Coordination of Heterogeneous Multiple Vehicle Systems

Kirchner,

Debord,

Hespanha

2020

Preprint

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We present a method for optimal coordination of multiple vehicle teams when multiple endpoint configurations are equally desirable, such as seen in the autonomous assembly of formation flight. The individual vehicles' positions in the formation are not assigned a priori and a key challenge is to find the optimal configuration assignment along with the optimal control and trajectory. Commonly, assignment and trajectory planning problems are solved separately. We introduce a new multi-vehicle coordination paradigm, where the optimal goal assignment and optimal vehicle trajectories are found simultaneously from a viscosity solution of a single Hamilton-Jacobi (HJ) partial differential equation (PDE), which provides a necessary and sufficient condition for global optimality. Intrinsic in this approach is that individual vehicle dynamic models need not be the same, and therefore can be applied to heterogeneous systems. Numerical methods to solve the HJ equation have historically relied on a discrete grid of the solution space and exhibits exponential scaling with system dimension, preventing their applicability to multiple vehicle systems. By utilizing a generalization of the Hopf formula, we avoid the use of grids and present a method that exhibits polynomial scaling in the number of vehicles.

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Section: Discussionmentioning

confidence: 99%

A Hamilton-Jacobi Formulation for Optimal Coordination of Heterogeneous Multiple Vehicle Systems

Kirchner,

Debord,

Hespanha

2020

Preprint

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“…The method can additionally be used to compute control inputs in order to complete an autonomous landing via autorotation. Future work includes augmenting (23) with human pilot dynamics as in McRuer and Krendel (1974) and include pilot reaction delay (Kirchner (2019)). Additionally, we will investigate integrating failure detection to initiate the autonomous autorotation landing procedure.…”

Section: Discussionmentioning

confidence: 99%

Reachability as a Unifying Framework for Computing Helicopter Safe Operating Conditions and Autonomous Emergency Landing

Kirchner,

Ball,

Hoffler

et al. 2020

Preprint

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We present a numeric method to compute the safe operating flight conditions for a helicopter such that we can ensure a safe landing in the event of a partial or total engine failure. The unsafe operating region is the complement of the backwards reachable tube, which can be found as the sub-zero level set of the viscosity solution of a Hamilton-Jacobi (HJ) equation. Traditionally, numerical methods used to solve the HJ equation rely on a discrete grid of the solution space and exhibit exponential scaling with dimension, which is problematic for the high-fidelity dynamics models required for accurate helicopter modeling. We avoid the use of spatial grids by formulating a trajectory optimization problem, where the solution at each initial condition can be computed in a computationally efficient manner. The proposed method is shown to compute an autonomous landing trajectory from any operating condition, even in non-cruise flight conditions.

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“…In fact, optimal control/controllability with respect to time delays is still an open problem: The current literature has addressed only a limited part of the problem, where the delays are constant valued and/or a priori fixed, and are not the main object of control. For example, we refer to [12][13] [14] for linear systems, and more recent work on nonlinear systems [15][16] [17]. In this paper, although we do not attempt to tackle this problem in its full generality, we introduce an approximation to nonlinear time-delay systems (TDS) that allows us to conveniently handle time-varying delay signals.…”

Section: Introductionmentioning

confidence: 99%

Towards cyber-physical systems robust to communication delays: A differential game approach

Deka¹,

Lee²,

Tomlin³

2021

Preprint

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Collaboration between interconnected cyberphysical systems is becoming increasingly pervasive. Timedelays in communication channels between such systems are known to induce catastrophic failure modes, like high frequency oscillations in robotic manipulators in bilateral teleoperation or string instability in platoons of autonomous vehicles. This paper considers nonlinear time-delay systems representing coupled robotic agents, and proposes controllers that are robust to timevarying communication delays. We introduce approximations that allow the delays to be considered as implicit control inputs themselves, and formulate the problem as a zero-sum differential game between the stabilizing controllers and the delays acting adversarially. The ensuing optimal control law is finally compared to known results from Lyapunov-Krasovskii based approaches via numerical experiments.

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A Level Set Approach to Online Sensing and Trajectory Optimization with Time Delays

Cited by 7 publications

References 18 publications

A Hamilton-Jacobi Formulation for Optimal Coordination of Heterogeneous Multiple Vehicle Systems

A Hamilton-Jacobi Formulation for Optimal Coordination of Heterogeneous Multiple Vehicle Systems

Reachability as a Unifying Framework for Computing Helicopter Safe Operating Conditions and Autonomous Emergency Landing

Towards cyber-physical systems robust to communication delays: A differential game approach

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