This paper presents a computational framework to efficiently generate feasible and safe trajectories for multiple autonomous vehicle operations. We formulate the optimal motion planning problem as a continuous-time optimal control problem, and approximate its solutions in a discretized setting using Bernstein polynomials. The latter possess convenient properties that allow to efficiently compute and enforce constraints along the vehicles trajectories, such as maximum speed and angular rates, minimum distance between trajectories and between the vehicles and known obstacles, etc. Thus, the proposed method is particularly suitable for generating trajectories in real-time for safe operations in complex environments and multiple vehicle missions. We show, using a rigorous mathematical framework, that the solution to the discretized optimal motion planning problem converges to that of the continuous-time one. The advantages of the proposed method are investigated through numerical examples.

This letter presents a computational framework to efficiently generate feasible and optimal trajectories for differentially flat autonomous vehicle systems. We formulate the optimal motion planning problem as a continuous-time optimal control problem, and approximate it by a discrete-time formulation using Bernstein polynomials. These polynomials allow for efficient computation of various constraints along the entire trajectory, and are particularly convenient for generating trajectories for safe operation of multiple vehicles in complex environments. The advantages of the proposed method are investigated through theoretical analysis and numerical examples.

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.

This article presents a computational framework for planning mine countermeasures (MCM) search missions by autonomous vehicles. It employs generalized optimal control (GenOC), a model-based trajectory optimization approach, to maximize the expected search performance of vehicle–sensor pairs in different minehunting scenarios. We describe each element of the proposed framework and adapt it to solve real-world MCM motion planning problems. A key contribution of this article develops sensor models that are more tunable than conventional ones based on lateral range curves. The proposed models incorporate engineering parameters and 3-D geometry to compute mine detection probability as a function of sonar design and search vehicle trajectories. Specific examples for various forward-looking and sidescan sonar systems deployed by unmanned vehicles are included. Objective computations utilize these sonar detection models during optimization to minimize the risk that candidate search trajectories fail to detect mines in an area of interest. Simulation results highlight the flexibility of our proposed GenOC framework and confirm that optimal trajectories outperform conventional search patterns under time or resource constraints. We conclude by identifying some of the practical considerations of this approach, and suggest ways that numerical analysis of GenOC solutions can be used for MCM mission planning and decision aid development.

This paper addresses the problem of optimal defense of a high-value unit (HVU) against a large-scale swarm attack. We discuss multiple models for intra-swarm cooperation strategies and provide a framework for combining these cooperative models with HVU tracking and adversarial interaction forces. We show that the problem of defending against a swarm attack can be cast in the framework of uncertain parameter optimal control. We discuss numerical solution methods, then derive a consistency result for the dual problem of this framework, providing a tool for verifying computational results. We also show that the dual conditions can be computed numerically, providing further computational utility. Finally, we apply these numerical results to derive optimal defender strategies against a 100-agent swarm attack.