Active Localization using Bernstein Distribution Functions

In this work, we present a framework that enables a vehicle to autonomously localize a target based on noisy range measurements computed from RSSI data. To achieve the mission objectives, we develop a control scheme composed of two main parts: an estimator and a motion planner. At each time step, new estimates of the target's position are computed and used to generate and update distribution functions using Bernstein polynomials. A metric of the efficiency of the estimator is derived based on the Fisher Information Matrix. Finally, the motion planning problem is formulated to react in real time to new information about the target and improve the estimator's performance.Comment: 6 page

Cooperative autonomous systems: Motion planning and coordinated tracking control for multi-vehicle missions

In this dissertation a framework for planning and control of cooperative autonomous systems is presented, which allows a group of Unmanned Vehicle Systems (UxSs) to generate and follow desired trajectories, while coordinating along them in order to satisfy relative temporal constraints. The described methodology is based on two key results. First, a centralized optimal motion planning algorithm produces a set of feasible and flyable trajectories, which guarantee inter-vehicle safety, while satisfying specific temporal mission requirements, as well as dynamic constraints of the vehicles. Then, a distributed coordinated tracking controller ensures that the vehicles follow the trajectories while coordinating along them in order to arrive at the final destination at the same time, or with a predefined temporal separation, according to the mission requirements. The optimal motion planning problem is formulated as a continuous-time optimal control problem, which is then approximated by a discrete-time formulation using Bernstein polynomials. Using the convergence properties of Bernstein polynomial approximation, the thesis provides a rigorous analysis that shows that the solution to the discrete-time approximation converges to the solution to the continuous-time problem. The motivation behind this approach lies in the fact that Bernstein polynomials possess favorable geometric properties that 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 coordinated tracking algorithm relies on the presence of a virtual target tracking controller which guarantees that the distance between each vehicle and its assigned virtual target running along the desired trajectory remains bounded throughout the mission. Then, the speed of the virtual target is adjusted in order to satisfy the temporal constraints and achieve coordination. The coordination problem is formulated as a consensus problem, with the objective of regulating a suitably defined set of coordination variables to zero. Conditions are derived under which the consensus algorithm proposed solves the coordination problem in the presence of faulty communications and switching topologies

Proximity Queries for Absolutely Continuous Parametric Curves

In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is generally non-convex and serves as a significant computational bottleneck for motion planning algorithms. In this paper, we present methods for a general class of absolutely continuous parametric curves to compute: (i) the minimum separating distance, (ii) tolerance verification, and (iii) collision detection. Our methods efficiently compute bounds on obstacle proximity by bounding the curve in a convex region. This bound is based on an upper bound on the curve arc length that can be expressed in closed form for a useful class of parametric curves including curves with trigonometric or polynomial bases. We demonstrate the computational efficiency and accuracy of our approach through numerical simulations of several proximity problems.Comment: Proceedings of Robotics: Science and System

Coordinated Path Following of UAVs over Time-Varying Digraphs Connected in an Integral Sense

This paper presents a new connectivity condition on the information flow between UAVs to achieve coordinated path following. The information flow is directional, so that the underlying communication network topology is represented by a time-varying digraph. We assume that this digraph is connected in an integral sense. This is a much more general assumption than the one currently used in the literature. Under this assumption, it is shown that a decentralized coordination controller ensures exponential convergence of the coordination error vector to a neighborhood of zero. The efficacy of the algorithm is confirmed with simulation results

Coordinated Path Following of UAVs using Event-Triggered Communication over Time-Varying Networks with Digraph Topologies

In this article, a novel time-coordination algorithm based on event-triggered communications is proposed to achieve coordinated path-following of UAVs. To be specific, in the approach adopted a UAV transmits its progression information over a time-varying network to its neighbors only when a decentralized trigger condition is satisfied, thereby significantly reducing the volume of inter-vehicle communications required when compared with the existing algorithms based on continuous communications. Using such intermittent communications, it is shown that a decentralized coordination controller guarantees exponential convergence of the coordination error to a neighborhood of zero. Also, a lower bound on the interval between two consecutive event-triggered times is provided showing that the chattering issue does not arise with the proposed algorithm. Finally, simulation results validate the efficacy of the proposed algorithm.Comment: arXiv admin note: text overlap with arXiv:2307.0655

Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems

The article of record as published may be found at http://dx.doi.org/10.3390/s22051869This 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/B�zier 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 research was supported by the Office of Naval Research, grants N000141912106, N000142112091 and N0001419WX00155. Antonio Pascoal was supported by H2020-EU.1.2.2-FET Proactive RAMONES, under Grant GA 101017808 and LARSyS-FCT under Grant UIDB/50009/2020. Isaac Kaminer was supported by the Office of Naval Research grant N0001421WX01974.This research was supported by the Office of Naval Research, grants N000141912106, N000142112091 and N0001419WX00155. Antonio Pascoal was supported by H2020-EU.1.2.2-FET Proactive RAMONES, under Grant GA 101017808 and LARSyS-FCT under Grant UIDB/50009/2020. Isaac Kaminer was supported by the Office of Naval Research grant N0001421WX01974