David W. Casbeer

David W. Casbeer, Yongcan Cao, Eloy Garcia et al.

In this paper, the problem of bridge consensus is presented and solved. Bridge consensus consists of a network of nodes, some of whom are participating and others are non-participating. The objective is for all the agents to reach average consensus of the participating nodes initial values in a distributed and scalable manner. To do this, the nodes must use the network connections of the non-participating nodes, which act as bridges for information and ignore the initial values of the non-participating nodes. The solution to this problem is made by merging the ideas from estimation theory and consensus theory. By considering the participating nodes has having equal information and the non-participating nodes as having no information, the nodes initial values are transformed into information space. Two consensus filters are run in parallel on the information state and information matrix. Conditions ensuring that the product of the inverse information matrix and the information state of each agent reaches average consensus of the participating agents' initial values is given.

Deepak Prakash Kumar, Swaroop Darbha, Satyanarayana Gupta Manyam et al.

In this paper, we propose a new modeling approach and a fast algorithm for 3D motion planning, applicable for fixed-wing unmanned aerial vehicles. The goal is to construct the shortest path connecting given initial and final configurations subject to motion constraints. Our work differs from existing literature in two ways. First, we consider full vehicle orientation using a body-attached frame, which includes roll, pitch, and yaw angles. However, existing work uses only pitch and/or heading angle, which is insufficient to uniquely determine orientation. Second, we use two control inputs to represent bounded pitch and yaw rates, reflecting control by two separate actuators. In contrast, most previous methods rely on a single input, such as path curvature, which is insufficient for accurately modeling the vehicle's kinematics in 3D. We use a rotation minimizing frame to describe the vehicle's configuration and its evolution, and construct paths by concatenating optimal Dubins paths on spherical, cylindrical, or planar surfaces. Numerical simulations show our approach generates feasible paths within 10 seconds on average and yields shorter paths than existing methods in most cases.

Sai Krishna Kanth Hari, Sivakumar Rathinam, Swaroop Darbha et al.

Persistent monitoring missions require an up-to-date knowledge of the changing state of the underlying environment. UAVs can be gainfully employed to continually visit a set of targets representing tasks (and locations) in the environment and collect data therein for long time periods. The enduring nature of these missions requires the UAV to be regularly recharged at a service station. In this paper, we consider the case in which the service station is not co-located with any of the targets. An efficient monitoring requires the revisit time, defined as the maximum of the time elapsed between successive revisits to targets, to be minimized. Here, we consider the problem of determining UAV routes that lead to the minimum revisit time. The problem is NP-hard, and its computational difficulty increases with the fuel capacity of the UAV. We develop an algorithm to construct near-optimal solutions to the problem quickly, when the fuel capacity exceeds a threshold. We also develop lower bounds to the optimal revisit time and use these bounds to demonstrate (through numerical simulations) that the constructed solutions are, on an average, at most 0.01% away from the optimum.

Sai Krishna Kanth Hari, Sivakumar Rathinam, Swaroop Darbha et al.

We consider the problem of planning a closed walk $\mathcal W$ for a UAV to persistently monitor a finite number of stationary targets with equal priorities and dynamically changing properties. A UAV must physically visit the targets in order to monitor them and collect information therein. The frequency of monitoring any given target is specified by a target revisit time, $i.e.$, the maximum allowable time between any two successive visits to the target. The problem considered in this paper is the following: Given $n$ targets and $k \geq n$ allowed visits to them, find an optimal closed walk $\mathcal W^*(k)$ so that every target is visited at least once and the maximum revisit time over all the targets, $\mathcal R(\mathcal W(k))$, is minimized. We prove the following: If $k \geq n^2-n$, $\mathcal R(\mathcal W^*(k))$ (or simply, $\mathcal R^*(k)$) takes only two values: $\mathcal R^*(n)$ when $k$ is an integral multiple of $n$, and $\mathcal R^*(n+1)$ otherwise. This result suggests significant computational savings - one only needs to determine $\mathcal W^*(n)$ and $\mathcal W^*(n+1)$ to construct an optimal solution $\mathcal W^*(k)$. We provide MILP formulations for computing $\mathcal W^*(n)$ and $\mathcal W^*(n+1)$. Furthermore, for {\it any} given $k$, we prove that $\mathcal R^*(k) \geq \mathcal R^*(k+n)$.

Satyanarayana Manyam, Sivakumar Rathinam, David Casbeer et al.

The Dubins interval problem aims to find the shortest path of bounded curvature between two targets such that the departure angle from the first target and the arrival angle at the second target are constrained to two respective intervals. We propose a new and a simple algorithm to this problem based on the minimum principle of Pontryagin.

Yongcan Cao, Jonathan Muse, David Casbeer et al.

This paper presents two control algorithms enabling a UAV to circumnavigate an unknown target using range and range rate (i.e., the derivative of range) measurements. Given a prescribed orbit radius, both control algorithms (i) tend to drive the UAV toward the tangent of prescribed orbit when the UAV is outside or on the orbit, and (ii) apply zero control input if the UAV is inside the desired orbit. The algorithms differ in that, the first algorithm is smooth and unsaturated while the second algorithm is non-smooth and saturated. By analyzing properties associated with the bearing angle of the UAV relative to the target and through proper design of Lyapunov functions, it is shown that both algorithms produce the desired orbit for an arbitrary initial state. Three examples are provided as a proof of concept.