This paper presents a unified approach to realize versatile distributed maneuvering with generalized formations. Specifically, we decompose the robots' maneuvers into two independent components, i.e., interception and enclosing, which are parameterized by two independent virtual coordinates. Treating these two virtual coordinates as dimensions of an abstract manifold, we derive the corresponding singularity-free guiding vector field (GVF), which, along with a distributed coordination mechanism based on the consensus theory, guides robots to achieve various motions (i.e., versatile maneuvering), including (a) formation tracking, (b) target enclosing, and (c) circumnavigation. Additional motion parameters can generate more complex cooperative robot motions. Based on GVFs, we design a controller for a nonholonomic robot model. Besides the theoretical results, extensive simulations and experiments are performed to validate the effectiveness of the approach.

Inverse kinematics is a fundamental technique for motion and positioning control in robotics, typically applied to end-effectors. In this paper, we extend the concept of inverse kinematics to guiding vector fields for path following in autonomous mobile robots. The desired path is defined by its implicit equation, i.e., by a collection of points belonging to one or more zero-level sets. These level sets serve as a reference to construct an error signal that drives the guiding vector field toward the desired path, enabling the robot to converge and travel along the path by following such a vector field. We start with the formal exposition on how inverse kinematics can be applied to guiding vector fields for single-integrator robots in an$m$-dimensional Euclidean space. Then, we leverage inverse kinematics to ensure that the level-set error signal behaves as a linear system, facilitating control over the robot's transient motion toward the desired path and allowing for the injection of feed-forward signals to induce precise motion behavior along the path. We then propose solutions to the theoretical and practical challenges of applying this technique to unicycles with constant speeds to follow 2D paths with precise transient control. We finish by validating the predicted theoretical results through real flights with fixed-wing drones.

The autonomous formation flight of fixed-wing drones is hard when the coordination requires the actuation over their speeds since they are critically bounded and aircraft are mostly designed to fly at a nominal airspeed. This paper proposes an algorithm to achieve formation flights of fixed-wing drones without requiring any actuation over their speed. In particular, we guide all the drones to travel over specific paths, e.g., parallel straight lines, and we superpose an oscillatory behavior onto the guiding vector field that drives the drones to the paths. This oscillation enables control over the average velocity along the path, thereby facilitating inter-drone coordination. Each drone adjusts its oscillation amplitude distributively in a closed-loop manner by communicating with neighboring agents in an undirected and connected graph. A novel consensus algorithm is introduced, leveraging a non-negative, asymmetric saturation function. This unconventional saturation is justified since negative amplitudes do not make drones travel backward or have a negative velocity along the path. Rigorous theoretical analysis of the algorithm is complemented by validation through numerical simulations and a real-world formation flight.

This paper focuses on coordinating a robot swarm orbiting a convex path without collisions among the individuals. The individual robots lack braking capabilities and can only adjust their courses while maintaining their constant but different speeds. Instead of controlling the spatial relations between the robots, our formation control algorithm aims to deploy a dense robot swarm that mimics the behavior of tornado schooling fish. To achieve this objective safely, we employ a combination of a scalable overtaking rule, a guiding vector field, and a control barrier function with an adaptive radius to facilitate smooth overtakes. The decision-making process of the robots is distributed, relying only on local information. Practical applications include defensive structures or escorting missions with the added resiliency of a swarm without a centralized command. We provide a rigorous analysis of the proposed strategy and validate its effectiveness through numerical simulations involving a high density of unicycles.

In this article, we propose coordinating guiding vector fields to achieve two tasks simultaneously with a team of robots: first, the guidance and navigation of multiple robots to possibly different paths or surfaces typically embedded in 2-D or 3-D, and second, their motion coordination while tracking their prescribed paths or surfaces. The motion coordination is defined by desired parametric displacements between robots on the path or surface. Such a desired displacement is achieved by controlling the virtual coordinates, which correspond to the path or surface's parameters, between guiding vector fields. Rigorous mathematical guarantees underpinned by dynamical systems theory and Lyapunov theory are provided for the effective distributed motion coordination and navigation of robots on paths or surfaces from all initial positions. As an example for practical robotic applications, we derive a control algorithm from the proposed coordinating guiding vector fields for a Dubins-car-like model with actuation saturation. Our proposed algorithm is distributed and scalable to an arbitrary number of robots. Furthermore, extensive illustrative simulations and fixed-wing aircraft outdoor experiments validate the effectiveness and robustness of our algorithm.

In this paper, we present an online planning-scheduling approach for battery-powered autonomous aerial robots. The approach consists of simultaneously planning a coverage path and scheduling onboard computational tasks. We further derive a novel variable coverage motion robust to air-borne constraints and an empirically motivated energy model. The model includes the energy contribution of the schedule based on an automatic computational energy modeling tool. Our experiments show how an initial flight plan is adjusted online as a function of the available battery, accounting for uncertainty. Our approach remedies possible in-flight failure in case of unexpected battery drops, e.g., due to adverse atmospheric conditions, and increases the overall fault tolerance.

It is essential in many applications to impose a scalable coordinated motion control on a large group of mobile robots, which is efficient in tasks requiring repetitive execution, such as environmental monitoring. In this paper, we design a guiding vector field to guide multiple robots to follow possibly different desired paths while coordinating their motions. The vector field uses a path parameter as a virtual coordinate that is communicated among neighboring robots. Then, the virtual coordinate is utilized to control the relative parametric displacement between robots along the paths. This enables us to design a saturated control algorithm for a Dubins-car-like model. The algorithm is distributed, scalable, and applicable for any smooth paths in an n-dimensional configuration space, and global convergence is guaranteed. Simulations with up to fifty robots and outdoor experiments with fixed-wing aircraft validate the theoretical results.

In robot navigation tasks, such as unmanned aerial vehicle (UAV) highway traffic monitoring, it is important for a mobile robot to follow a specified desired path. However, most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-intersected desired paths due to the existence of singular points where navigation algorithms return unreliable or even no solutions. One typical example arises in vector-field guided path-following (VF-PF) navigation algorithms. These algorithms are based on a vector field, and the singular points are exactly where the vector field diminishes. Conventional VF-PF algorithms generate a vector field of the same dimensions as those of the space where the desired path lives. In this article, we show that it is mathematically impossible for conventional VF-PF algorithms to achieve global convergence to desired paths that are self-intersected or even just simple closed (precisely, homeomorphic to the unit circle). Motivated by this new impossibility result, we propose a novel method to transform self-intersected or simple closed desired paths to nonself-intersected and unbounded (precisely, homeomorphic to the real line) counterparts in a higher dimensional space. Corresponding to this new desired path, we construct a singularity-free guiding vector field on a higher dimensional space. The integral curves of this new guiding vector field is thus exploited to enable global convergence to the higher dimensional desired path, and therefore the projection of the integral curves on a lower dimensional subspace converge to the physical (lower dimensional) desired path. Rigorous theoretical analysis is carried out for the theoretical results using dynamical systems theory. In addition, we show both by theoretical analysis and numerical simulations that our proposed method is an extension combining conventional VF-PF algorithms and trajectory tracking algorithms. Finally, to show the practical value of our proposed approach for complex engineering systems, we conduct outdoor experiments with a fixed-wing airplane in windy environment to follow both 2-D and 3-D desired paths.

We propose a combined method for the collaborative transportation of a suspended payload by a team of rotorcraft. A recent distance-based formation-motion control algorithm based on assigning distance disagreements among robots generates the acceleration signals to be tracked by the vehicles. In particular, the proposed method does not need global positions nor tracking prescribed trajectories for the motion of the members of the team. The acceleration signals are followed accurately by an Incremental Nonlinear Dynamic Inversion controller designed for rotorcraft that measures and resists the tensions from the payload. Our approach allows us to analyze the involved accelerations and forces in the system so that we can calculate the worst case conditions explicitly to guarantee a nominal performance, provided that the payload starts at rest in the 2D centroid of the formation, and it is not under significant disturbances. For example, we can calculate the maximum safe deformation of the team with respect to its desired shape. We demonstrate our method with a team of four rotorcraft carrying a suspended object two times heavier than the maximum payload for an individual. Last but not least, our proposed algorithm is available for the community in the open-source autopilot Paparazzi.

In this paper, we present the design and implementation of a robust motion formation distributed control algorithm for a team of mobile robots. The primary task for the team is to form a geometric shape, which can be freely translated and rotated at the same time. This approach makes the robots to behave as a cohesive whole, which can be useful in tasks such as collaborative transportation. The robustness of the algorithm relies on the fact that each robot employs only local measurements from a laser sensor which does not need to be off-line calibrated. Furthermore, robots do not need to exchange any information with each other. Being free of sensor calibration and not requiring a communication channel helps the scaling of the overall system to a large number of robots. In addition, since the robots do not need any off-board localization system, but require only relative positions with respect to their neighbors, it can be aimed to have a full autonomous team that operates in environments where such localization systems are not available. The computational cost of the algorithm is inexpensive and the resources from a standard microcontroller will suffice. This fact makes the usage of our approach appealing as a support for other more demanding algorithms, e.g., processing images from onboard cameras. We validate the performance of the algorithm with a team of four mobile robots equipped with low-cost commercially available laser scanners.

This paper presents an algorithm for solving the problem of tracking smooth curves by a fixed wing unmanned aerial vehicle travelling with a constant airspeed and under a constant wind disturbance. The algorithm is based on the idea of following a guiding vector field which is constructed from the implicit function that describes the desired (possibly time-varying) trajectory. The output of the algorithm can be directly expressed in terms of the bank angle of the UAV in order to achieve coordinated turns. Furthermore, the algorithm can be tuned offline such that physical constraints of the UAV, e.g. the maximum bank angle, will not be violated in a neighborhood of the desired trajectory. We provide the corresponding theoretical convergence analysis and performance results from actual flights.

In this paper we propose an algorithm for stabilizing circular formations of fixed-wing UAVs with constant speeds. The algorithm is based on the idea of tracking circles with different radii in order to control the inter-vehicle phases with respect to a target circumference. We prove that the origin of the error dynamics of the inter-vehicle phases is exponentially stable. Furthermore, thanks to the stability properties of the guidance vector field that guides the vehicles, the algorithm can be extended to other closed trajectories. One of the main advantages of this approach is that the algorithm guarantees the confinement of the team in a specific area, even when communications or sensing among vehicles are lost. We show the effectiveness of the algorithm with an actual formation flight of three aircraft. The algorithm is ready to use for the general public in the open-source Paparazzi autopilot.

Recently, it has been reported that inconsistent range-measurement or, equivalently, mismatches in prescribed interagent distances, may prevent popular gradient controllers from guiding rigid formations of mobile agents to converge to their desired shape and, even worse, from standing still at any location. In this paper, instead of treating mismatches as the source of poor performance, we take them as design parameters and show that by introducing such a pair of parameters per distance constraint, distributed controller achieving simultaneously both formation and motion control can be designed that not only encompasses the popular gradient control, but more importantly allows us to achieve constant collective translation, rotation, or their combination, while guaranteeing asymptotically that no distortion in the formation shape occurs. Such motion control results are then applied to 1) the alignment of formations' orientations and 2) enclosing and tracking a moving target. Besides rigorous mathematical proof, experiments using mobile robots are demonstrated to show the satisfying performances of the proposed formation-motion distributed controller.

Despite the great success of using gradient-based controllers to stabilize rigid formations of autonomous agents in the past years, surprising yet intriguing undesirable collective motions have been reported recently, when inconsistent measurements are used in the agents' local controllers. To make the existing gradient control robust against such measurement inconsistency, we exploit local estimators following the well-known internal model principle for robust output regulation control. The new estimator-based gradient control is still distributed in nature, and can be constructed systematically even when the number of agents in a rigid formation grows. We prove rigorously that the proposed control is able to guarantee exponential convergence, and then demonstrate through robotic experiments and computer simulations that the reported inconsistency-induced orbits of collective movements are effectively eliminated.

This paper studies the performances of the popular gradient-based formation-control strategies for teams of autonomous agents when the agents' range measurements are coarse. Since the dynamics of the resulting closed-loop system are discontinuous, Filippov solutions to non-smooth dynamical systems are introduced. Similar to the existing stability results for triangular formations with precise range measurements, we prove that under coarse range measurements, the convergence to the desired formation is almost global except for initially collinearly positioned formations. More importantly, we are able to make stronger statements that the convergence takes place within finite time and that the settling time can be determined by the geometric information of the initial shape of the formation. Simulation and experimental results are provided to validate the theoretical analysis.

A sea demining system using autonomous marine surface vehicles (AMSV) is introduced. The research involves the development of exemplars of these vehicles, and the procedures for area scanning and coverage. The demining is made by field influence, towing a submerged “fish”. This study is made both with simulations and with scale experiments.