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 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 paper presents a theoretical framework for augmenting an existing autopilot by an adaptive element so that it tracks a given smooth reference command with desired specifications. The main contribution of the approach is that it allows for augmenting the autopilot without any modifications to it. The augmentative adaptive element is based on the L₁ adaptive output feedback control architecture developed in [1]. The complete path following architecture of this paper enables a UAV with an off-the-shelf autopilot to follow a predetermined path that it was not otherwise designed to follow. The paper concludes with flight test results performed in Camp Roberts, CA, in February of 2007.

A considerable volume of research has recently blossomed in the literature on autonomous underwater vehicles accepting recent developments in mathematical modeling and system identification; pitch control; information filtering and active sensing, including inductive sensors of ELF emissions and also optical sensor arrays for position, velocity, and orientation detection; grid navigation algorithms; and dynamic obstacle avoidance, amongst others. In light of these modern developments, this article develops and compares integrative guidance, navigation, and control methodologies for the Naval Postgraduate School’s Phoenix submerged autonomous vehicle, where these methods are assumed available. The measure of merit reveals how well each of several proposed methodologies cope with known and unknown disturbances, such as currents that can be constant or harmonic, while maintaining a safe passage distance from underwater obstacles, in this case submerged mines. Classical pole-placement designs establish nominal baseline behaviors and are subsequently compared to performance of designs that are optimized to satisfy linear quadratic cost functions in regulators as well as linear-quadratic Gaussian designs. Feed-forward architectures and integral control designs are also evaluated. A noteworthy contribution is a very simple method to mimic optimal results with a “rule of thumb” criteria based on the design’s time constant. Since the rule-of-thumb method uses the assumed system model for computation of the control, it is particularly generic. Cited references each contain methods for online system parameter identification (with a motivation of use in the finding the control signal), permitting the rule of thumb’s generic applicability, since it is expressed in terms of the system parameters. This proposed method permits control design at sea where significant computation abilities are not available. Very simple waypoint guidance is also introduced to guide a vehicle along a preplanned path through a field of obstacles placed at random locations. The linear-quadratic Gaussian design proves best when augmented with integral control, and works well with reduced-order equations, while the “rule of thumb” design is seen to closely mimic the optimal performance. Feed-forward augmentation proves particularly efficient at rejecting constant disturbances, while augmentation with integral control is necessary to counter periodic disturbances, where the augmentations are also optimized in the linear-quadratic Gaussian procedures, yet can be closely mimicked by the proposed “rule of thumb” technique.

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.