Approximation of reachable sets using optimal control algorithms

Baier, Robert; Gerdts, Matthias; Xausa, Ilaria

doi:10.3934/naco.2013.3.519

Cited by 63 publications

(56 citation statements)

References 51 publications

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“…In [2] it is shown that the approximation PR h,k convergences in the Hausdorff distance to PR of order O(h + k) as h and k approach zero, if PR is closed and non-empty. Direct discretization techniques for the numerical solution of the optimal control problem introduce a further approximation to PR h,k whose convergence properties for a special setting are analyzed in [2] as well. The projected reachable set approximations PR h,k are depicted in Figure 3 for different initial velocities and the data y min = 1.3, y max = 5.7, d min = 10, d max = 200, y 0 = 1.75, F B,min = −5000, F B,max = 15000.…”

Section: Approach 2: Computing the Projected Reachable Setmentioning

confidence: 99%

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Avoidance Trajectories Using Reachable Sets and Parametric Sensitivity Analysis

Gerdts

Xausa

2013

IFIP Advances in Information and Communication Technology

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Abstract. The article suggests a conceptual model-based simulation method with the aim to detect collision of cars in all-day road traffic. The benefit of the method within a driver assistance system would be twofold. Firstly, unavoidable accidents could be detected and appropriate actions like full braking maneuvers could be initiated in due course. Secondly, in case of an avoidable accident the algorithm is able to suggest an evasion trajectory that could be tracked by a future active steering driver assistance system. The algorithm exploits numerical optimal control techniques and reachable set analysis. A parametric sensitivity analysis is employed to investigate the influence of inaccurate sensor measurements.

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Section: Approach 2: Computing the Projected Reachable Setmentioning

confidence: 99%

“…In order to approximate the projected reachable set we employ the optimal control technique in [1,2], which for a simplified setting allows a first order approximation. The set PR is approximated as follows.…”

Section: Approach 2: Computing the Projected Reachable Setmentioning

confidence: 99%

Avoidance Trajectories Using Reachable Sets and Parametric Sensitivity Analysis

Gerdts

Xausa

2013

IFIP Advances in Information and Communication Technology

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“…In this section, the DFOG algorithm developed by Baier et al in [19,22] used for the computation of the reachable sets is explained. First it is explained how the DFOG method uses optimal control problems to compute an approximation to the reachable set.…”

Section: Distance Fields Over Grids Algorithmmentioning

confidence: 99%

“…The main contribution of this research is the application of DFOG, [19], to flight envelope determination. To achieve this, two extensions were made to the existing DFOG algorithm to increase its computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

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Distance-Fields-Over-Grids Method for Aircraft Envelope Determination

Helsen

Kampen

Visser

et al. 2016

Journal of Guidance, Control, and Dynamics

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In this research, the concept of posing the flight envelope as a reachable set is explored further and it is investigated whether the "Distance Fields Over Grids (DFOG)" method for reachability computations is a viable method for envelope determination.The DFOG method approximates the reachable set of a dynamic system by solving a number of optimal control problems over a grid in the state-space. Then, the end-

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Computation of avoidance regions for driver assistance systems by using a Hamilton‐Jacobi approach

Xausa

Baier

Bokanowski

et al. 2020

Optim Control Appl Methods

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Summary We consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time‐dependent obstacles. The Hamilton‐Jacobi‐Bellman framework is used. A new formulation of level set functions for obstacle avoidance is given, and sufficient conditions for granting the obstacle avoidance on the whole time interval are obtained even though the conditions are checked only at discrete times. Different scenarios, including various road configurations, different geometry of vehicle and obstacles, as well as fixed or moving obstacles, are then studied and computed. Computations involve solving nonlinear partial differential equations of up to five space dimensions plus time with nonsmooth obstacle representations, and an efficient solver is used to this end. A comparison with a direct optimal control approach is also done for one of the examples.

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Approximation of reachable sets using optimal control algorithms

Cited by 63 publications

References 51 publications

Avoidance Trajectories Using Reachable Sets and Parametric Sensitivity Analysis

Avoidance Trajectories Using Reachable Sets and Parametric Sensitivity Analysis

Distance-Fields-Over-Grids Method for Aircraft Envelope Determination

Computation of avoidance regions for driver assistance systems by using a Hamilton‐Jacobi approach

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