A fast motion planning algorithm for car parking based on static optimization

Zips, Patrik; Böck, Martin; Kugi, Andreas

doi:10.1109/iros.2013.6696692

Cited by 15 publications

(10 citation statements)

References 15 publications

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“…7 as an example. Thus, the object o's I-stability increases 3 whenever one of the following increases (ceteris paribus): Before we briefly comment on each of these points, we introduce a formal definition of a function I-stability : O → [0, 1] that assigns to each object an I-stability value from the interval [0, 1] (where 0 means that the object will move without any stimuli and 1 means that the object is impossible to move).…”

Section: I-stabilitymentioning

confidence: 98%

Qualitative Physics in <italic>Angry Birds</italic>

Wałęga

Zawidzki

Lechowski

2016

IEEE Trans. Comput. Intell. AI Games

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In this paper, we present a program designed to successfully and autonomously play Angry Birds which attempts to embrace motives of human players in their choices of targets they want to shoot at in a game play. The program comprises two modules: the representation module and the reasoning module. In the former we introduce qualitative space representation that utilises notions such as "to lie on", "to lie to the right", "to be a shelter of a target", etc. The latter investigates how particular blocks of a structure behave once one of them has been hit. It includes two algorithms, namely Vertical Impact and Horizontal Impact. The first one is a novel method of investigating the behaviour of complex structures after one of their constituent blocks gets hit. Namely, it predicts which elements of a structure fall if a supporting block gets destroyed. Horizontal Impact, on the other hand, simulates force propagation between adjacent elements after one of them gets struck. We also describe experimental tests we have conducted in which Vertical Impact correctly predicted which blocks will fall in over 98% of investigated cases.

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Section: I-stabilitymentioning

confidence: 98%

Qualitative Physics in <italic>Angry Birds</italic>

Wałęga

Zawidzki

Lechowski

2016

IEEE Trans. Comput. Intell. AI Games

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“…Meanwhile, the typical controlspace samplers include the hybrid A * algorithm [13], and the dynamic window approach [14]. As the second category, optimization-based methods describe a trajectory planning task as an optimal control problem (OCP) and discretize it into a nonlinear programming (NLP) problem [15], [16]. Samplingand-search-based planners are good at choosing the homotopy class globally (e.g., left or right around each of the obstacles) while optimization-based planners are superior in finding a local optimum while keeping the homotopy class not altered.…”

Section: B Related Workmentioning

confidence: 99%

“…Herein, z * is defined as the expanded state profile, i.e., [z, x f , y f , x r , y r ]; the geometric relation equation ( 12) is taken as part of the interior kinematic principle of the ego vehicle. In contrast with (11), the dimension of ( 16) is fully irrelevant to the complexity of the environment, which means that the number of constraints in (16) does not alter no matter how large N OBS is. By solving (16) numerically, collocation points that represent a parking trajectory are derived.…”

Section: Within-corridor Constraint Formulationmentioning

confidence: 99%

“…The preceding section has presented how to simplify the nominal OCP (11) into an easier version (16). However, ( 16) is subject to the following issues.…”

Section: A Motivationsmentioning

confidence: 99%

“…Due to the first issue, solving (16) renders a near-optimal rather than an optimal solution when the optimum falls into the uncovered regions. The second issue may make (16) fail to be solved if the constructed corridors do not cover any kinematically feasible trajectory. To summarize, directly solving ( 16) is not always reliable.…”

Section: A Motivationsmentioning

confidence: 99%

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Optimization-Based Trajectory Planning for Autonomous Parking With Irregularly Placed Obstacles: A Lightweight Iterative Framework

Acarman

Zhang

et al. 2022

IEEE Trans. Intell. Transport. Syst.

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This paper is focused on planning fast, accurate, and optimal trajectories for autonomous parking. Nominally, this task should be described as an optimal control problem (OCP), wherein the collision-avoidance constraints guarantee travel safety and the kinematic constraints guarantee tracking accuracy. The dimension of the nominal OCP is high because it requires the vehicle to avoid collision with each obstacle at every moment throughout the entire parking process. With a coarse trajectory guiding a homotopic route, the intractably scaled collision-avoidance constraints are replaced by within-corridor constraints, whose scale is small and independent from the environment complexity. Constructing such a corridor sacrifices partial free spaces, which may cause loss of optimality or even feasibility. To address this issue, our proposed method reconstructs the corridor in an iterative framework, where a lightweight OCP with only box constraints is quickly solved in each iteration. The proposed planner, together with several prevalent optimization-based planners are tested under 115 simulation cases w.r.t. the success rate and computational time. Real-world indoor experiments are conducted as well.

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