Abstract
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.
Highlights
The field of autonomous guidance has exploded in the past decade
This progress has led to high demand for computationally efficient algorithms that may yield safe and optimal trajectories to be planned for groups of autonomous vehicles
Our proposed method aims to accomplish these tasks by formulating the optimal trajectory generation problem as a nonlinear programming problem and exploiting the useful features of Bernstein polynomials
Summary
The field of autonomous guidance has exploded in the past decade. Significant progress has been made in self driving vehicles, bringing them one step closer to reality [1]. In contrast to closed-loop methods, open-loop methods can generate solutions in one-shot for the whole mission time, and are able to present an operator with an intuitive representation of the future trajectory This representation is typically shown as a 2D or 3D path and may include speed, acceleration, and higher derivatives of the vehicle’s motion. Our goal is to introduce a method that mitigates this trade-off, and that provides provably safe solutions for high dimensional problems while retaining the computational efficiency of low-order trajectory planning algorithms. This is achieved by exploiting the useful features of Bernstein polynomials. Our method for trajectory generation builds upon [36–38], where Bernstein polynomials were introduced as a tool to approximate the solutions of nonlinear optimal control problems with provable convergence guarantees.
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