BeBOT: Bernstein Polynomial Toolkit for Trajectory Generation

Kielas-Jensen, Calvin; Cichella, Venanzio

doi:10.1109/iros40897.2019.8967564

Cited by 19 publications

(16 citation statements)

References 29 publications

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“…For the interested reader, an open-source implementation is provided. This paper extends the results initially presented in [39]. In particular, in [39] we focused on autonomous vehicle trajectories representation by Bernstein polynomials, and proposed a preliminary implementation of BeBOT for minimum distance computation and collision detection for safe autonomous operation.…”

Section: Introductionmentioning

confidence: 55%

“…This paper extends the results initially presented in [39]. In particular, in [39] we focused on autonomous vehicle trajectories representation by Bernstein polynomials, and proposed a preliminary implementation of BeBOT for minimum distance computation and collision detection for safe autonomous operation. In the present paper, we extend previous work by exploiting properties and proposing algorithms for both Bernstein polynomials and rational Bernstein polynomials.…”

Section: Introductionmentioning

confidence: 55%

“…Here we will examine several illustrative examples of the properties of Bernstein polynomials and rational Bernstein polynomials in 2D. All the plots presented can be generated using the example code available at [40].…”

Section: D Trajectoriesmentioning

confidence: 99%

“…We added a new algorithm, the penetration algorithm, and several additional examples including air traffic control, navigation of a cluttered environment, vehicle overtaking, 1000 vehicle swarming, a marine vehicle example, and two examples of a vehicle routing problem. An implementation of the examples presented in this paper is available at our GitHub website [40] and can be customized to facilitate the toolbox's usability.…”

Section: Introductionmentioning

confidence: 99%

“…The paper ends with Section 6, which draws some conclusions. A Python implementation of the properties and algorithms presented, as well as the scripts used to generate the plots and examples found throughout this paper, can be found on our GitHub webpage [40].…”

mentioning

confidence: 99%

See 4 more Smart Citations

Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems

Kielas-Jensen

Cichella

Berry

et al. 2022

Sensors

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This paper presents a method for the generation of trajectories for autonomous system operations. The proposed method is based on the use of Bernstein polynomial approximations to transcribe infinite dimensional optimization problems into nonlinear programming problems. These, in turn, can be solved using off-the-shelf optimization solvers. The main motivation for this approach is that Bernstein polynomials possess favorable geometric properties and yield computationally efficient algorithms that enable a trajectory planner to efficiently evaluate and enforce constraints along the vehicles’ trajectories, including maximum speed and angular rates as well as minimum distance between trajectories and between the vehicles and obstacles. By virtue of these properties and algorithms, feasibility and safety constraints typically imposed on autonomous vehicle operations can be enforced and guaranteed independently of the order of the polynomials. To support the use of the proposed method we introduce BeBOT (Bernstein/Bézier Optimal Trajectories), an open-source toolbox that implements the operations and algorithms for Bernstein polynomials. We show that BeBOT can be used to efficiently generate feasible and collision-free trajectories for single and multiple vehicles, and can be deployed for real-time safety critical applications in complex environments.

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Section: Introductionmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 55%

Section: D Trajectoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems

Kielas-Jensen

Cichella

Berry

et al. 2022

Sensors

Self Cite

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Persistent Monitoring by Multiple Unmanned Aerial Vehicles Using Bernstein Polynomials

Kielas-Jensen

Cichella

Casbeer

et al. 2021

J Optim Theory Appl

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Optimal Kinodynamic Trajectory Planner for Mobile Robots in an Unknown Environment Using Bézier Contours

Mazen,

Faied,

Krishnan

2024

IEEE Access

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Trajectory planning in the field of mobile robotics involves the generation of a trajectory to navigate a robot from a start state to a goal state. One widely employed technique involves a twostep approach: a path planner generates a path made up of piecewise linear segments with sharp turns, which are then smoothed in the trajectory generation step. In contrast, this work formulates trajectory generation as an optimization problem based on the Bézier curve, denoted as 'BTP', to generate the robot's trajectory in one step. It uses a weighted objective function to adopt different optimization strategies, while considering the robot kinematics and dynamics limitations. BTP adopts matrix-based formulations for all mathematical operations to enable dynamic adjustment of the degree of the Bézier curve during the optimization process, if convergence is not obtained with the current degree. Additionally, BTP guarantees that the robot's trajectory is always within the open space identified by the robot's sensors. The efficacy of BTP has been evaluated through simulations and real-world experimentation using different scenarios and objective functions. Finally, the performance is benchmarked against some of the existing trajectory planners.

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BeBOT: Bernstein Polynomial Toolkit for Trajectory Generation

Cited by 19 publications

References 29 publications

Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems

Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems

Persistent Monitoring by Multiple Unmanned Aerial Vehicles Using Bernstein Polynomials

Optimal Kinodynamic Trajectory Planner for Mobile Robots in an Unknown Environment Using Bézier Contours

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