This work addresses the problem of radially segregating heterogeneous robotic swarms. Such swarms are those composed of different groups of robots. Unlike other works on segregation in the literature, we propose a controller for Dubins-like robots, motivated by autonomous aerial, wheeled, and underwater vehicles. Our controller can drive the robots individually to converge to circles that are shared only by robots of the same group. We present a heuristic and a collision avoidance scheme in which the information required is locally acquired. We present several simulations widely varying the number of robots per group and the number of groups in which segregation is always reached and collisions between robots are always avoided.

This paper introduces a motion planning approach for navigating in a dynamic environment. The path is represented using a Non-Uniform Rational B-Spline (NURBS) to ensure smoothness, curvature continuity, and proper orientation by adjusting its parameters. A Differential Evolution algorithm optimizes the curve parameters and traversal speed at each replanning interval, taking into account speed limits, maximum curvature, and obstacles in the environment. A constraintbased on Velocity Obstacle (VO) ensures collision-free motion, considering bounds provided by lower-level controllers. The feasibility of the approach is validated through simulations and real-world experiments with the Crazyflie 2.1 micro quadcopter.

In this work, we present an Integrated Guidance and Controller (IGC) scheme to drive quadcopters in path-following tasks with obstacle avoidance and constant uncertainty rejection. This scheme is based on the combination of a time-varying artificial vector field and Backstepping with integral action control. The vector field switches between two behaviors: (i) path-following; and (ii) obstacle circumnavigation to allow collision avoidance. This vector field is then integrated into a nonlinear controller designed via Backstepping with Integral Action to deal with the quadcopter vehicle dynamics and reject constant uncertainties. The considered vehicle model is based on quaternion algebra. The control inputs are considered to be the total thrust and torques. Stability is proved by using Lyapunov's Theory and Matrosov's Theorem.

This paper proposes a task planning and motion control framework that generates task plans for a linear temporal logic specification (LTL), which are then executed using a task-space constrained motion controller and a local task planner that overcomes local minima. We propose a new encoding for task specifications, directly in the task-space, as constraints of a mixed-integer linear program that can be used with off-the-shelf LTL linear encoding. We apply our framework to plan and execute trajectories for a free-flying robot and show that the task plan is accomplished without collisions, even in the presence of unexpected moving obstacles that are not considered in the planning phase, while control signal constraints are satisfied. To evaluate the local minima avoidance, we compare the local task planner with a sampling-based motion planner, and the results show a smoother trajectory with a faster execution and less total planning time when using our framework. Last, our framework scaled well with a longer LTL specification, as opposed to automata-based frameworks that usually suffer with the curse of the dimensionality.

In this work, we present a methodology to compute an artificial time-varying vector field in$n$dimensions that defines trajectories that converge to and follow a given desired curve. The Euclidean distance function is used to construct the field, which is easily computed from a parametric representation of the curve. The computation of the time feedforward term to compensate for time dependence is such that its norm is limited by the maximum velocity of the curve. This fact allows the normalization of the time-varying vector field such that it has a constant norm without any negative effect for convergence. We present convergence proofs for the proposed normalized time-varying vector field and demonstrate the existence of ultimate bounds in the case bounded disturbances are present. Finally, we show several simulations and experiments with an actual quadrotor to validate our methodology.

The present work focuses on the development of an efficient path controller to guide a fixed-wing UAV (Unmanned Aerial Vehicle) to follow a closed curve and avoid unknown dynamic obstacles. Our strategy is composed of two layers: a top level layer responsible for guidance and a lower level layer responsible for tracking the references given by the top level. To solve the guidance problem, we propose a vector field strategy that switches between two forms: a vector field to converge and circulate the target curve and a vector field to avoid obstacles by circulating the closest one. To make the fixed-wing UAV follow the velocity provided by the guidance vector field we consider a Model Predictive Control scheme. The feedback linearization allows efficient computation of control commands as a linear MPC controller can be employed. Our results are validated in simulations that take into account the 6DOF (Degrees of Freedom) model with constraints of the aircraft, wind disturbance and uncertainties on the measurements.

This paper proposes a decentralized control strategy to reach segregation in heterogeneous robot swarms distributed in curves. The approach is based on a formation control algorithm applied to each robot and a heuristics to compute the distance between the groups, i.e. the distance from the beginning of the curve. We consider that robots can communicate through a fixed underlying topology and also when they are within a certain distance. A convergence proof with a collision avoidance strategy is presented. Simulations and experimental results show that our approach allows a swarm of multiple heterogeneous robots to segregate into groups.

This article presents a path tracking control strategy for a quadcopter to follow a time varying curve. The control is based on artificial vector fields. The construction of the field is based on a well known technique in the literature. Next, control laws are developed to impose the behavior of the vector field to a second order integrator model. Finally, control laws are developed to impose the dynamics of the controlled second order integrator to a quadcopter model, which assumes the thrust and the angular rates as input commands. Asymptotic convergence of the whole system is proved by showing that the individual systems in cascade connection are input-to-state stable. We also analyze the influence of norm-bounded disturbances in the control inputs to evaluate the robustness of the controller. We show that bounded disturbances originate limited deviations from the target curve. Simulations and a real robot experiment exemplify and validate the developed theory.

This paper presents a guidance vector field strategy to control a fixed-wing UAV (unmanned aerial vehicle)subject to uncertainty in order to converge to and circulate a closed curve in ℝ3. The control system is designed based on a reference model of the airplane with constrained input controls. The law is independent of the vector field's structure, however, some analysis considers a consolidated vector field approach. Asymptotic stability is proven with Lyapunov Theory and ultimate bounds are found when bounded uncertainties are taken into account. The control law is continuous except in the surroundings of the unavoidable field's singularities. A theorem ensures asymptotic convergence when a switch is made. Simulations with a 6 DOF, 12 states realistic aircraft model demonstrate the efficiency of the strategy and its advantages.

In this work, multiple robots circulate around the boundary of a desired region in order to create a virtual fence. The aim of the this fence is to avoid internal or external agents crossing through the delimited area. In this paper, we propose a distributed technique that allows a team of robots to plan the deformation of the boundary shape in order to escort the safe region from one place to a goal. Our proposal is composed of two parts. First, we present a distributed planning method for the dynamic boundary. We model the resulting plan as a twice differentiable function. Second, we use the obtained function to guide the robot team, where every member uses only local information for the controller. The robots distribute themselves along the time-varying perimeter and patrol around it. We show in simulation how the robots behave in partially/totally unknown environments with static obstacles.

In this paper, we propose a motion planning method to escort a set of agents from one place to a goal in an environment with obstacles. The agents are distributed in a finite area, with a time-varying perimeter, in which we put multiple robots to patrol around it with a desired velocity. Our proposal is composed of two parts. The first one generates a plan to move and deform the perimeter smoothly, and as a result, we obtain a twice differentiable boundary function. The second part uses the boundary function to compute a trajectory for each robot, we obtain each resultant trajectory by first solving a differential equation. After receiving the boundary function, the robots do not need to communicate among themselves until they finish their trajectories. We validate our proposal with simulations and experiments with actual robots.

This paper proposes a new approach for a group of robots carrying out a collaborative task to adapt on-line to actuation performance variations among the robots. We consider the problem of multi-robot coverage, where a group of robots has to spread out to cover the environment. We suppose that some robots have poor actuation performance (e.g. weak motors, friction losses in the gear train, wheel slip, etc.) and some have strong actuation performance (powerful motors, little friction, favorable terrain, etc.). The robots do not know before hand the relative strengths of their actuation compared to the others in the team. The algorithm in this paper learns the relative actuation performance variations among the robots on-line, in a distributed fashion, and automatically compensates by giving the weak robots a small portion of the environment, and giving the strong robots a larger portion. Using a Lyapunov-type proof, we prove that the robots converge to locally optimal positions for coverage. The algorithm is demonstrated in both Matlab simulations and experiments using Pololu m3pi robots.

This paper addresses the problem of segregation of groups of heterogeneous units in robot swarms. We propose a controller that can drive robots in a way that each group composed of robots of a similar type will form clusters while maintaining segregation from other groups. The approach is based on abstractions created to represent each group of robots and an artificial potential function used to segregate the groups. Different from previous works on swarm segregation, we can mathematically guarantee that by using our approach the system will always converge to a state where multiple dissimilar groups are segregated. Moreover, in some situations, our controller does not require all robots to have information about all the other robots in the system. We demonstrate the effectiveness of our controller with simulations with different types of robots and varying number of robots and groups.

Several natural systems adopt self-sorting mechanisms based on segregative behaviors. Among these, cell segregation is of particular interest since it plays an important role in the formation of tissues, organs, and living organisms. The Differential Adhesion Hypothesis states that cells naturally segregate because of differences in affinity, which lead similar cells to strongly adhere to each other. By exploring this principle, we propose a controller that can segregate a heterogeneous swarm of robots according to the characteristics of each agent, such that similar robots form homogeneous teams and dissimilar robots are segregated. We apply LaSalle's Invariance Principle to show convergence and perform simulated experiments in order to demonstrate the robustness and effectiveness of the proposed controller. Results show that our approach allows a swarm of multiple heterogeneous robots to segregate in a coherent and smooth fashion, without any inter-agent collisions.

This paper addresses the problem of coordinating the motion of multiple fixed-wing Unmanned Aerial Vehicles (UAVs) following closed intersecting curves. We require that each UAV avoid collisions with its teammates without changing its predefined, periodic path. Also, each robot must keep a minimum speed to avoid stall and a maximum speed determined by its physical constraints. The centralized solution presented in this paper is modeled as a Mixed Integer Linear Programming (MILP) problem. The solution to this problem, which maximizes safeness (in the sense of collision avoidance), determines, for each UAV, the start time and the velocity profile over the curve.

The focus of this study is on the design of feedback control laws for swarms of robots that are based on models from fluid dynamics. We apply an incompressible fluid model to solve a pattern generation task. Possible applications of an efficient solution to this task are surveillance and the cordoning off of hazardous areas. More specifically, we use the smoothed-particle hydrodynamics (SPH) technique to devise decentralized controllers that force the robots to behave in a similar manner to fluid particles. Our approach deals with static and dynamic obstacles. Considerations such as finite size and nonholonomic constraints are also addressed. In the absence of obstacles, we prove the stability and convergence of controllers that are based on the SPH method. Computer simulations and actual robot experiments are shown to validate the proposed approach.

Different robotic tasks can be solved by controlling a robot to circulate along curves. These include, for example, border inspection and surveillance, multirobot manipulation, and pattern generation. In a previous, work we have proposed a vector field approach for robot convergence and circulation along time-varying curves embedded in N-dimensional spaces. In the present work we instantiate this approach for three-dimensional spaces and, for the first time, show the efficacy of this method to control actual robots. Besides new theoretical analysis when constant speed control is applied, we present experimental results with aerial (quadrotors) and ground (differential-driven) robot.

This paper presents a methodology for computation of artificial vector fields that allows a robot to converge to and circulate around generic curves specified in$n$-dimensional spaces. These vector fields may be directly applied to solve several robot-navigation problems such as border monitoring, surveillance, target tracking, and multirobot pattern generation, with special application to fixed-wing aerial robots, which must keep a positive forward velocity and cannot converge to a single point. Unlike previous solutions found in the literature, the approach is based on fully continuous vector fields and is generalized to time-varying curves defined in$n$-dimensional spaces. We provide mathematical proofs and present simulation and experimental results that illustrate the applicability of the proposed approach. We also present a methodology for construction of the target curve based on a given set of its samples.

We address the problem of pattern generation in obstacle-filled environments by a swarm of mobile robots. Decentralized controllers are devised by using the Smoothed Particle Hydrodynamics (SPH) method. The swarm is modelled as an incompressible fluid subjected to external forces. Actual robot issues such as finite size and nonholonomic constraints are also addressed. Collision avoidance guarantees are discussed. Finally, in the absence of obstacles, we prove for the first time stability and convergence of controllers based on the SPH.

Several recent works have combined discrete and continuous motion planning methods for robot navigation and control. The basic idea of some of these works is to plan a path, by determining a sequence of neighboring discrete regions of the configuration space, and to assign a vector field that drives the robots through these regions. This paper addresses the problem of efficiently computing vector fields over a sequence of consecutive triangles. Differently from previous numerical approaches, which were not able to compute fully continuous fields in triangulated spaces, this paper presents an algorithm that is able to compute guaranteed continuous vector fields over a sequence of adjacent triangles.

This paper presents a comparative study of six encodings which have been used to represent trees in evolutionary algorithms. The study has been divided into two steps: 1) The encoding methods have been evaluated taking into account the time necessary to perform operations such as decoding, crossover and mutation, the feasibility of solutions after those operations, and the corresponding heritability and locality; 2) The encoding methods have been employed in a genetic algorithm to solve three different instances (with 10, 25 and 50 nodes) of the optimal communication spanning tree problem. Finally, the results obtained with each of the encodings are statistically compared using Kruskal-Wallis non-parametric tests and multiple comparisons. The results of this study provide insight into the properties of current encoding schemes for network design problems.

This paper addresses the problem of efficiently computing robot navigation functions. Navigation functions are potential functions free of spurious local minima that present an exact solution to the robot motion planning and control problem. Although some methodologies were found in the literature, none of them are easy to implement and generalize for complex shaped workspaces and robots. We discuss some of the difficulties encountered in the current methodologies and propose a novel approach using a Finite Element method for potential field computation.