A practical path-planning algorithm for a simple car: a Hamilton-Jacobi approach

Takei, Ryo; Tsai, Richard; Shen, Haochong; Landa, Yanina

doi:10.1109/acc.2010.5531607

Cited by 41 publications

(35 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• Ship orientation: A specific task will typically require a vehicle to have a particular orientation, especially its heading at the end position [40]. This applies to the close-range maneuvering task when the ship is approaching the oil rig.…”

Section: A Close-range Maneuveringmentioning

confidence: 99%

See 1 more Smart Citation

Toward Time-Optimal Trajectory Planning for Autonomous Ship Maneuvering in Close-Range Encounters

Hildre

Zhang

2020

IEEE J. Oceanic Eng.

View full text Add to dashboard Cite

Ship intelligence has been a hot topic in recent years. How to achieve autonomous maneuvers in a complex marine environment in a safe, efficient, and low-cost manner is a fundamental task that ocean engineers face. This paper presents a two-stage trajectory planning scheme to address the minimumtime maneuvering problem in close-range encounters. The scheme is robust and versatile, as it can deal with the complex spatial variability, such as sea current, state constraints, marine traffic, and physical constraints, of close-range maneuvering. In the first stage, a directed graph with variable length is generated according to the sea current distribution. A wavefront search is applied on the graph to explore the reachability, the cost of state constraints, and the risk of collision. After a discrete solution has been found, the second stage involves searching for a smooth solution. A Bézier curve based parameter optimization approach is proposed to get rid of limited moving directions in the directed graph and explore around the discrete path. The result will be a near-optimal, smooth path. The proposed scheme has been tested to solve the Zermelo's ship steering problem and several other close-range maneuvering problems. The results demonstrate that the scheme is efficient in generating smoothed minimum-time trajectories for surface vessels when maneuvering in close-range encounters.

show abstract

Section: A Close-range Maneuveringmentioning

confidence: 99%

“…Complete initial/final states may make the problem unsolvable. Relaxing the constraints by involving only partial initial/final states, such as X, (X, φ), or (X, θ), renders a solution to (4) possible [40].…”

Section: Remarkmentioning

confidence: 99%

Toward Time-Optimal Trajectory Planning for Autonomous Ship Maneuvering in Close-Range Encounters

Hildre

Zhang

2020

IEEE J. Oceanic Eng.

View full text Add to dashboard Cite

show abstract

“…These so-called Dubins' cars were constrained by a maximum turning radius so Dubins considered paths with bounded local curvature [7]. Recently, this problem was reformulated using a Hamilton-Jacobi-Bellman equation and adapted to include impassable obstacles [1,33]. Indeed, Hamilton-Jacobi-Bellman (HJB) equations are now used extensively in optimal path problems.…”

Section: Introductionmentioning

confidence: 99%

Optimal human navigation in steep terrain: a Hamilton–Jacobi–Bellman approach

Parkinson

Arnold

Bertozzi

et al. 2019

Communications in Mathematical Sciences

View full text Add to dashboard Cite

We present a method for determining optimal walking paths in steep terrain using the level set method and an optimal control formulation. By viewing the walking direction as a control variable, we can determine the optimal control by solving a Hamilton-Jacobi-Bellman equation. We then calculate the optimal walking path by solving an ordinary differential equation. We demonstrate the effectiveness of our method by computing optimal paths which travel throughout mountainous regions of Yosemite National Park. We include details regarding the numerical implementation of our model and address a specific application of a law enforcement agency patrolling a nationally protected area.

show abstract

“…Sethian and Vladimirsky [19,20] discuss a level set method for optimal travel on manifolds. In application, Dubins [5], and later Takei et al [21], modeled movement of simple cars through terrain with obstacles using methods from control theory which include Hamilton-Jacobi-Bellman equations. Tomlin has used similar methods to determine reachable sets for aircraft autolanders [2], and to model human movement in adversarial reach-avoid games [24].…”

Section: Introductionmentioning

confidence: 99%

Modeling Environmental Crime in Protected Areas Using the Level Set Method

Arnold¹,

Fernandez²,

Jia³

et al. 2019

SIAM J. Appl. Math.

View full text Add to dashboard Cite

National parks often serve as hotspots for environmental crime such as illegal deforestation and animal poaching. Previous attempts to model environmental crime were either discrete and network-based or required very restrictive assumptions on the geometry of the protected region and made heavy use of radial symmetry. We formulate a level set method to track criminals inside a protected region which uses real elevation data to determine speed of travel, does not require any assumptions of symmetry, and can be applied to regions of arbitrary shape. In doing so, we design a Hamilton-Jacobi equation to describe movement of criminals while also incorporating the effects of patrollers who attempt to deter the crime. We discuss the numerical schemes that we use to solve this Hamilton-Jacobi equation. Finally, we apply our method to Yosemite National Park and Kangaroo Island, Australia and design practical patrol strategies with the goal of minimizing the area that is affected by criminal activity.

show abstract

A practical path-planning algorithm for a simple car: a Hamilton-Jacobi approach

Cited by 41 publications

References 24 publications

Toward Time-Optimal Trajectory Planning for Autonomous Ship Maneuvering in Close-Range Encounters

Toward Time-Optimal Trajectory Planning for Autonomous Ship Maneuvering in Close-Range Encounters

Optimal human navigation in steep terrain: a Hamilton–Jacobi–Bellman approach

Modeling Environmental Crime in Protected Areas Using the Level Set Method

Contact Info

Product

Resources

About