Obstacle avoidance using hierarchical dynamic programming

Peterson, James K.

doi:10.1109/ssst.1991.138545

Cited by 5 publications

(5 citation statements)

References 11 publications

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“…Then, Algorithm 21 terminates in a finite number of steps depending on ε and Z. Upon termination, it identifies the discrete spline trajectory that connects eachẑ ∈ A to the target τ in the fewest number of steps while minimizing the secondary objective function (2). Furthermore, Algorithm 22 used for motion replanning from a given start state σ ∈ W k σ , k σ ≥ 1, terminates in at most k max = (τ ) + 1 2 ( (σ ) − (τ )) ( (σ ) + (τ ) − 3) iterations after recomputing the optimal trajectory from σ to τ .…”

Section: Lemma 19mentioning

confidence: 99%

“…The optimization problem associated with most motion planning tasks is inherently non-convex 1 and difficult to solve. 2 The non-convexity of the problem is a direct consequence of the obstacle avoidance requirement and is further complicated by inclusion of the state and actuation constraints. Furthermore, changing and/or uncertain obstacle fields, which arise in most real-world applications, pose additional challenges in achieving the required solution to this problem.…”

Section: Introductionmentioning

confidence: 99%

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Dual objective motion planning subject to state constraints

Sadegh

2015

Robotica

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SUMMARYThis paper presents a novel motion planning approach inspired by the Dynamic Programming (DP) applicable to multi degree of freedom robots (mobile or stationary) and autonomous vehicles. The proposed discrete–time algorithm enables a robot to reach its destination through an arbitrary obstacle field in the fewest number of time steps possible while minimizing a secondary objective function. Furthermore, the resulting optimal trajectory is guaranteed to be globally optimal while incorporating state constraints such as velocity, acceleration, and jerk limits. The optimal trajectories furnished by the algorithm may be further updated in real time to accommodate changes in the obstacle field and/or cost function. The algorithm is proven to terminate in a finite number of steps without its computational complexity increasing with the type or number of obstacles. The effectiveness of the global and replanning algorithms are demonstrated on a planar mobile robot with three degrees of freedom subject to velocity and acceleration limits. The computational complexity of the two algorithms are also compared to that of an A*–type search.

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Section: Lemma 19mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dual objective motion planning subject to state constraints

Sadegh

2015

Robotica

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“…Paths prefer coarse level cells which approximate the original data better. Somewhat closer to our strategy, [28] uses a filtering method to obtain coarse level information from the finer levels in the context of obstacle avoidance using dynamic programming.…”

Section: A Related Workmentioning

confidence: 99%

Multiresolution rough terrain motion planning

Pai

Reissell

1998

IEEE Trans. Robot. Automat.

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We describe a new approach to the problem of motion planning for mobile robots on natural, rough terrain. Our approach computes a multiresolution representation of the terrain using wavelets, and hierarchically plans the path through sections which are well approximated on coarser levels and relatively smooth. Unlike most methods, the hierarchical approximation errors are used explicitly in a cost function to distinguish preferred terrain sections. The error is computed using the corresponding wavelet coefficients. We also propose a new nonscalar path cost measure based on the sorted terrain costs along the path. This measure can be incorporated into standard global path search algorithms and yields paths which avoid high cost terrain areas when possible. Additional constraints for specific robots can be integrated into this approach for efficient hierarchical motion planning on rough terrain. We present the algorithms and experimental results for real terrain data.

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“…This paper presents a discrete-time Time-Optimal motion planning algorithm based on the Dynamic Programming (DP) approach [10]. The existing works on the applications of DP to path planning can be found in [2], [11], [12], [13]. In particular, the approach pursued in [12] is the one most closely related to the present work.…”

Section: Introductionmentioning

confidence: 96%

“…The optimization problem associated with most path planning tasks is inherently non-convex [1] and difficult to solve [2]. The non-convexity of the problem is a direct consequence of the obstacle avoidance requirement and is further complicated by the inclusion of the state and actuation constraints.…”

Section: Introductionmentioning

confidence: 99%

Time-optimal motion planning of autonomous vehicles in the presence of obstacles

Sadegh

2008

2008 American Control Conference

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Abstract-This paper presents a novel motion planning approach inspired by the Dynamic Programming (DP) for mobile robots and other autonomous vehicles. The proposed discretetime algorithm enables a multi-degree of freedom vehicle to reach its destination through an arbitrary obstacle field in a minimum number of time steps. Furthermore, the resulting optimal path is guaranteed to posses the required degree of smoothness and incorporates the motion state constraints such as velocity, acceleration, and jerk limits. The algorithm is proven to terminate in a finite number of steps without its computational complexity increasing with the type or number of obstacles. The effectiveness of the algorithm is demonstrated on a mobile robot modeled as a point-mass in a 2-dimensional space subject to velocity and acceleration limits.

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Obstacle avoidance using hierarchical dynamic programming

Cited by 5 publications

References 11 publications

Dual objective motion planning subject to state constraints

Dual objective motion planning subject to state constraints

Multiresolution rough terrain motion planning

Time-optimal motion planning of autonomous vehicles in the presence of obstacles

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