Motion Planning for Highly Constrained Spaces

Yershova, Anna; LaValle, Steven M.

doi:10.1007/978-1-84882-985-5_27

Cited by 22 publications

(17 citation statements)

References 15 publications

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“…state spaces in cluttered environments. Instead of providing completeness guarantees, these algorithms provide probabilistic completeness in the sense that the probability of failing to return a solution, if one exits, decays to zero as the number of samples approaches infinity [76][77][78][79][80][81][82][83].…”

Section: Sampling-based Algorithmsmentioning

confidence: 99%

- Residual Gas and Stochastic Control

Shen¹,

Zhang²,

Jiao³

et al. 2015

Transient Control of Gasoline Engines

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Controlling dynamical systems in uncertain environments is fundamental and essential in several fields, ranging from robotics, healthcare to economics and finance. In these applications, the required tasks can be modeled as continuous-time, continuous-space stochastic optimal control problems. Moreover, risk management is an important requirement of such problems to guarantee safety during the execution of control policies. However, even in the simplest version, finding closed-form or exact algorithmic solutions for stochastic optimal control problems is comuputationally challenging.The main contribution of this thesis is the development of theoretical foundations, and provably-correct and efficient sampling-based algorithms to solve stochastic optimal control problems in the presence of complex risk constraints.In the first part of the thesis, we consider the mentioned problems without risk constraints. We propose a novel algorithm called the incremental Markov Decision Process (iMDP) to compute incrementally any-time control policies that approximate arbitrarily well an optimal policy in terms of the expected cost. The main idea is to generate a sequence of finite discretizations of the original problem through random sampling of the state space. At each iteration, the discretized problem is a Markov Decision Process that serves as am incrementally refined model of the original problem. We show that the iMDP algorithm guarantees asymptotic optimality while maintaining low computational and space complexity.In the second part of the thesis, we consider risk constraints that are expressed as either bounded trajectory performance or bounded probabilities of failure. For the former, we present the first extended iMDP algorithm to approximate arbitrarily well an optimal feedback policy of the constrained problem. For the latter, we present a martingale approach that diffuses a risk constraint into a martingale to construct time-consistent control policies. The martingale stands for the level of risk tolerance that is contingent on available information over time. By augmenting the system dynamics with the martingale, the original risk-constrained problem is transformed into a stochastic target problem. We present the second extended iMDP algorithm to approximate arbitrarily well an optimal feedback policy of the original problem by sampling in the augmented state space and computing proper boundary values for the reformulated problem. In both cases, sequences of policies returned from the extended algorithms are both probabilistically sound and asymptotically optimal.

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Section: Sampling-based Algorithmsmentioning

confidence: 99%

- Residual Gas and Stochastic Control

Shen¹,

Zhang²,

Jiao³

et al. 2015

Transient Control of Gasoline Engines

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“…Another possibility is to focus the sampling on a subset of the ambient space around the configuration space (Yershova and LaValle, 2009). However, even in the case where the configuration is properly bounded, samples are thrown in the ambient space that can be of much higher dimensionality than the configuration space.…”

Section: Related Workmentioning

confidence: 99%

Randomized path planning on manifolds based on higher-dimensional continuation

Porta

Jaillet

Bohigas

2011

The International Journal of Robotics Research

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Despite the significant advances in path planning methods, highly constrained problems are still challenging. In some situations, the presence of constraints defines a configuration space that is a non-parametrizable manifold embedded in a high dimensional ambient space. In these cases, the use of sampling-based path planners is cumbersome since samples in the ambient space have low probability to lay on the configuration space manifold. In this paper, we present a new path planning algorithm specially tailored for highly constrained systems. The proposed planner builds on recently developed tools for higher-dimensional continuation, which provide numerical procedures to describe an implicitly defined manifold using a set of local charts. We propose to extend these methods focussing the generation of charts on the path between the two configurations to connect and randomizing the process to find alternative paths in the presence of obstacles. The advantage of this planner comes from the fact that it directly operates into the configuration space and not into the higher-dimensional ambient space, as most of the existing methods do.

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“…To improve the quality of the sampling, one can focus on a subset of the ambient space around the configuration space [44]. However, with this method points are still sampled in the ambient space, which can be of much higher dimensionality than the configuration space.…”

Section: Introductionmentioning

confidence: 99%

Path Planning with Loop Closure Constraints Using an Atlas-Based RRT

Jaillet

Porta

2016

Springer Tracts in Advanced Robotics

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In many relevant path planning problems, loop closure constraints reduce the configuration space to a manifold embedded in the higher-dimensional joint ambient space. Whereas many progresses have been done to solve path planning problems in the presence of obstacles, only few work consider loop closure constraints. In this paper, we present the AtlasRRT algorithm, a planner specially tailored for such constrained systems that builds on recently developed tools for higher-dimensional continuation. These tools provide procedures to define charts that locally parametrize manifolds and to coordinate them forming an atlas. Atlas-RRT simultaneously builds an atlas and a Rapidly-Exploring Random Tree (RRT), using the atlas to sample relevant configurations for the RRT, and the RRT to devise directions of expansion for the atlas. The advantage of the new planner comes from that samples obtained from the atlas allow a more efficient extension of the RRT as compared to state of the art approaches where samples are generated in the joint ambient space.

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Motion Planning for Highly Constrained Spaces

Cited by 22 publications

References 15 publications

- Residual Gas and Stochastic Control

- Residual Gas and Stochastic Control

Randomized path planning on manifolds based on higher-dimensional continuation

Path Planning with Loop Closure Constraints Using an Atlas-Based RRT

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