Dissertation
BeBOT: Bernstein polynomial-based method for solving complex optimal motion planning problems
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Autumn 2023
DOI: 10.25820/etd.007021
Abstract
This thesis 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. In particular, it is shown that by approximating the vehicles' states and inputs using Bernstein polynomials, typical trajectory generation problems for autonomous vehicles can be formulated as 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. It is shown 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.
Details
- Title: Subtitle
- BeBOT: Bernstein polynomial-based method for solving complex optimal motion planning problems
- Creators
- Calvin Jensen
- Contributors
- Venanzio Cichella (Advisor)Rachel Vitali (Committee Member)Shaoping Xiao (Committee Member)Casey Harwood (Committee Member)Adam Rutkowski (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Mechanical Engineering
- Date degree season
- Autumn 2023
- Publisher
- University of Iowa
- DOI
- 10.25820/etd.007021
- Number of pages
- x, 127 pages
- Copyright
- Copyright 2023 Calvin Jensen
- Comment
This thesis has been optimized for improved web viewing. If you require the original version, contact the University Archives at the University of Iowa: https://www.lib.uiowa.edu/sc/contact/.
- Language
- English
- Date submitted
- 08/03/2023
- Description illustrations
- Illustrations, graphs, charts
- Description bibliographic
- Includes bibliographical references (pages 117-127).
- Public Abstract (ETD)
In this dissertation, a groundbreaking method for generating trajectories in autonomous systems is unveiled. Imagine self-driving cars and drones navigating through complex environments smoothly and safely – this research brings us one step closer to that reality. The novel approach revolves around using Bernstein polynomials, a mathematical concept that makes trajectory planning more efficient and robust.
By approximating the states and inputs of autonomous vehicles with these polynomials, we convert complex optimization problems into simpler ones that can be efficiently solved using standard tools. The key advantage lies in Bernstein polynomials’ inherent geometric properties, which enable precise evaluation and enforcement of constraints, like maximum speed, angular rates, and safe distances from obstacles and other vehicles.
Safety is paramount in autonomous vehicle operations. With this method, we ensure that feasibility and safety constraints are met, regardless of the complexity of the trajectory. We introduce BeBOT, an open-source toolbox implementing the operations and algorithms needed to put this technique into action. BeBOT empowers autonomous vehicles to generate feasible and collision-free trajectories in real-time, even in intricate and challenging environments.
This research opens doors for revolutionizing autonomous systems and paves the way for safer and more efficient transportation. As we deploy BeBOT and explore its capabilities, we gain greater confidence in the potential of autonomous vehicles to navigate the world seamlessly, making our cities smarter, safer, and more sustainable for the future.
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984546944202771
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