Robot Formation Research Articles

ROBOT FORMATION MODELLING AND CONTROL BASED ON THE RELATIVE KINEMATICS EQUATIONS

This paper deals with the problem of modeling, initialization, and control of mobile robots formation. We suggest to use a new family of methods that consists of a combination between classical guidance laws and kinematics rules. These methods allow modeling and controlling a dynamic robotic formation using sets of differential equations that give the relative motion between the robots. These differential equations give the range rate and the visibility angle between leaders and followers. Graph theory is used to store the relationship leader-follower and plan the formation by using three different matrices. The configuration of the formation is based on these matrices. Initialization of formation is also considered, where different approaches are suggested. Because of the nature of the kinematics laws, it is easy to model, initialize, and keep any formation shape. Simulation is provided to illustrate the method.

Reactive multi-agent based control of mobile robot chain formations

A Multi-agent based coordination scheme for chain formations of mobile robots, employing geometric constraint satisfaction rules, is presented. Applying this architecture on mobile robot swarms, snake-like real-time motion and reactive obstacle avoidance is achieved. A “Master – Slave” relationship is used, where a controller agent's motion is propagated to its two neighbouring ones in the chain formation and progressively further on towards the two chain endpoints. At each propagation step, a constraint preservation mechanism enforces the respect of minimum and maximum (minmax) distance constraint between agent pairs, and of minmax angular constraint among triplets of consecutive chain agents. The emergent behaviour of this multi-agent system is as if a moving part of the chain pushes or pulls the two subparts it divides the chain into. To allow replaning in case a slave part can't adapt to its master's motion, being trapped in obstacles or malfunctioning, the notion of a “Vetoable slave” behaviour is used, where the slave part can object (veto) to the motion of its master part.

Stabilization of Nonholonomic Robot Formations: A First-state Contractive Model Predictive Control Approach

A model predictive control algorithm is developed for stabilizing a team of nonholonomic mobile robots navigating in formation within an obstacle-populated environment. In this scenario, the {\em leader} robot may need to execute abrupt maneuvers (i.e., sudden stops and backward motions) in order to avoid collisions and accomplish mission objectives. Moreover, follower robots should be capable of tracking their leaders maintaining desired relative distance and orientation. To this end, nonholonomic trajectory tracking and point stabilization should be combined in a suitable way. Most proposed control algorithms for nonholonomic robots do not have simultaneous tracking and point stabilization capability; therefore, they may perform poorly when the leader robot executes aggressive maneuvers. In this paper, we address this problem by applying model predictive control (MPC). Motivated by the contractive MPC scheme developed in [14], the proposed algorithm guarantees its stability by adding a contractive constraint on the first state at the beginning of the prediction horizon. The resulting MPC scheme is denoted as first-state contractive MPC (FSC-MPC). In the absence of disturbances, it can be shown that the control algorithm is stable and can achieve some practical formations without any special treatments. Simulation results are provided to verify the effectiveness of the method.

Semiautonomous control of multiple networked Lagrangian systems

AbstractIn this paper we study the problem of coordinating the positions of a group of Lagrangian systems with communication constraints exhibited through delays and limited data rates. We show that in a bidirectional connected communication graph structure, it is possible to design PD‐type control laws that render the overall nonnetworked system input‐to‐state stable. Then, we exploit the robustness property of these control laws along with a small‐gain condition on the allowable delays to infer the stability of the overall networked system. We illustrate how the obtained results can be specialized to handle the problem of position–position control for three networked 2DOF manipulators as well as teleoperation of robotic formations. Copyright © 2008 John Wiley & Sons, Ltd.

Circle formation of weak mobile robots

We consider distributed systems made of weak mobile robots, that is, mobile devices, equipped with sensors, that are anonymous , autonomous , disoriented , and oblivious . The Circle Formation Problem (CFP) consists of the design of a protocol insuring that, starting from an initial arbitrary configuration where no two robots are at the same position, all the robots eventually form a regular n-gon —the robots take place on the circumference of a circle C with equal spacing between any two adjacent robots on C . CFP is known to be unsolvable by arranging the robots evenly along the circumference of a circle C without leaving C —that is, starting from a configuration where the robots are on the boundary of C . We circumvent this impossibility result by designing a scheme based on concentric circles . This is the first scheme that deterministically solves CFP. We present our method with two different implementations working in the semi-synchronous system (SSM) for any number n ≥ 5 of robots.

Artificial moment method for swarm robot formation control

The purpose of this paper is to develop a general control method for swarm robot formation control. Firstly, an attraction-segment leader-follower formation graph is presented for formation representations. The model of swarm robot systems is described. According to the results and two kinds of artificial moments defined as leader-attraction moment and follower-attraction moment, a novel artificial moment method is proposed for swarm robot formation control. The principle of the method is introduced and the motion controller of robots is designed. Finally, the stability of the formation control system is proved. The simulations show that both the formation representation graph and the formation control method are valid and feasible.

Dynamic model based formation control and obstacle avoidance of multi-robot systems

SUMMARYThis work presents, first, a complete dynamic model of a unicycle-like mobile robot that takes part in a multi-robot formation. A linear parameterization of this model is performed in order to identify the model parameters. Then, the robot model is input-output feedback linearized. On a second stage, for the multi-robot system, a model is obtained by arranging into a single equation all the feedback linearized robot models. This multi-robot model is expressed in terms of formation states by applying a coordinate transformation. The inverse dynamics technique is then applied to design a formation control. The controller can be applied both to positioning and to tracking desired robot formations. The formation control can be centralized or decentralized and scalable to any number of robots. A strategy for rigid formation obstacle avoidance is also proposed. Experimental results validate the control system design.

Using Sensor Morphology for Multirobot Formations

In formation-maintenance (formation control) tasks, robots maintain their relative position with respect to their peers, according to a desired geometric shape. Previous work has examined formation-maintenance algorithms, based on formation control graphs, that ensure the theoretical stability of the formation. However, an exponential number of stable controllers exists. Thus a key question is how to select (construct) a formation controller that optimizes desired properties, such as sensor usage. We present a novel representation of the sensing capabilities of robots in formations, using a monitoring multigraph. We first show that graph-theoretic techniques can then be used to efficiently compute optimal sensing policies that maintain a given formation, while minimizing sensing costs. In particular, separation-bearing (distance-angle) control targets are automatically constructed for each individual robot in the formation, taking into account its specific sensor morphology. Then, we present a protocol allowing control graphs to be switched on line, to allow robots to adjust to sensory failures. We report on results from comprehensive experiments with physical and simulated robots. The results show that the use of the dynamic protocol allows formations of real robots to move significantly faster and with greater precision, while reducing the number of formation failures, due to sensor limitations. We also evaluate the sensitivity of our approach to communication reliability, and discuss opportunities and challenges raised by our approach.

Leader–follower formation control of nonholonomic mobile robots with input constraints

The paper deals with leader–follower formations of nonholonomic mobile robots, introducing a formation control strategy alternative to those existing in the literature. Robots’ control inputs are forced to satisfy suitable constraints that restrict the set of leader possible paths and admissible positions of the follower with respect to the leader. A peculiar characteristic of the proposed strategy is that the follower position is not rigidly fixed with respect to the leader but varies in proper circle arcs centered in the leader reference frame.

1A1-F03 IETアルゴリズムを用いた複数ロボットの編隊移動に関する研究(群ロボットの協調制御)

This paper describes the IET(Imaginary Equilateral Triangle) algorithm which can allocate each robot on the desired position in the swarm without global coordinate. The IET algorithm forms the swarm by making the equilateral triangles with the neighbors specified by vector. Through some simulation experiments, the convergence to the formation by the IET algorithm is confirmed and the convergence time is also evaluated. Furthermore, we tested the parallel and rotational movement of the formation.

A Learning Approach to Enable Locomotion of Multiple Robotic Agents Operating in Natural Terrain Environments

Abstract This paper presents a methodology that utilizes soft computing approaches to enable locomotion of multiple legged robotic agents operating in natural terrain environrnents. For individual robotic control, the locomotion strategy consists of a hybrid FSM-GA approach that couples leg orientation states with a genetic algorithm to leazn necessary leg movement sequences. To achieve multi-agent formations, locomotion behavior is driven by using a trained neural network to extract relevant distance metrics necessary to realize desired robotic formations while operating in the field. These distance metrics aze then fed into local controllers for realizing lineaz and rotational velocity values for each robotic agent. Details of the methodology are discussed, and experimental results with a team of mobile robots aze presented.

Convex Optimization Strategies for Coordinating Large-Scale Robot Formations

This paper investigates convex optimization strategies for coordinating a large-scale team of fully actuated mobile robots. Our primary motivation is both algorithm scalability as well as real-time performance. To accomplish this, we employ a formal definition from shape analysis for formation representation and repose the motion planning problem to one of changing (or maintaining) the shape of the formation. We then show that optimal solutions, minimizing either the total distance or minimax distance the nodes must travel, can be achieved through second-order cone programming techniques. We further prove a theoretical complexity for the shape problem of O(m1.5) as well as O(m) complexity in practice, where m denotes the number of robots in the shape configuration. Solutions for large-scale teams (1000's of robots) can be calculated in real time on a standard desktop PC. Extensions integrating both workspace and vehicle motion constraints are also presented with similar complexity bounds. We expect these results can be generalized for additional motion planning tasks, and will prove useful for improving the performance and extending the mission lives of large-scale robot formations as well as mobile ad hoc networks.

Motion Planning for Nonlinear Symmetric Distributed Robotic Formations

This paper develops a motion planning algorithm which exploits symmetries in distributed systems to reduce motion planning computation complexity. Symmetries allow for algebraic manipulations that are computationally costly, which normally must be carried out for each component in a distributed system, to be related among various symmetric components in a distributed system by a simple algebraic relationship. This leads to a large reduction in the complexity of the overall motion planning problem for a group of distributed mobile robotic agents. In particular, due to the manner in which a symmetric system is defined, the structure of the Chen—Fliess—Sussmann differential equations has a simple relationship among various symmetric components of a distributed system. Essentially, symmetries are defined in a manner which preserves the Lie algebraic structure of each component. In a system with distributed computational capability, the motion planning computations may be distributed throughout formation in such a way that the objectives of the formation are satisfied and collision avoidance is guaranteed. The algorithm maintains a rigid body formation at the beginning and end of the trajectory, as well as possibly specified intermediate points. Due to the generally nonholonomic nature of mobile robots, guaranteeing a rigid body formation during the intermediate motion is impossible. However, it is possible to bound the magnitude of the deviation from the rigid body formation at any point along the trajectory. Simulation and experimental results are provided to demonstrate the utility of the algorithm.

Robust Leader-follower Formation Control of Mobile Robots Based on a Second Order Kinematics Model

In this paper, we study the problem of modeling and controlling leader-follower formation of mobile robots. First, a novel kinematics model for leader-follower robot formation is formulated based on the relative motion states between the robots and the local motion of the follower robot. Using this model, the relative centripetal and Coriolis accelerations between robots are computed directly by measuring the relative and local motion sensors, and utilized to linearize the nonlinear system equations. A formation controller, consisting of a feedback linearization part and a sliding mode compensator, is designed to stabilize the overall system including the internal dynamics. The control gains are determined by solving a robustness inequality and assumed to satisfy a cooperative protocol that guarantees the stability of the zero dynamics of the formation system. The proposed controller generates the commanded acceleration for the follower robot and makes the formation control system robust to the effect of unmeasured acceleration of the leader robot. Furthermore, a robust adaptive controller is developed to deal with parametric uncertainty in the system. Simulation and experimental results have demonstrated the effectiveness of the proposed control method.

Localization With Limited Sensing

Localization is a fundamental problem for many kinds of mobile robots. Sensor systems of varying ability have been proposed and successfully used to solve the problem. This paper probes the lower limits of this range by describing three extremely simple robot models and addresses the active localization problem for each. The robot, whose configuration is composed of its position and orientation, moves in a fully-known, simply connected polygonal environment. We pose the localization task as a planning problem in the robot's information space, which encapsulates the uncertainty in the robot's configuration. We consider robots equipped with: 1) angular and linear odometers; 2) a compass and contact sensor and; 3) an angular odometer and contact sensor. We present localization algorithms for models 1 and 2 and show that no algorithm exists for model 3. An implementation with simulation examples is presented.

Decentralized control of mobile robots in formation

A control scheme for mobile robot formation in the leader following mode is proposed. It enables to track the target and is based on using a sliding mode along the desired trajectory in the state space. Results of modeling using MATLAB/SIMULINK environment are presented. They confirm efficiency of the proposed algorithm.

A Dynamic Regulation and Scheduling Scheme for Formation Control

This article is concerned with cooperative control problems in formation of mobile robots under the nonholonomic constraints that certain geometrical constraints are imposed on multiple mobile robots throughout their travel. For this purpose, a new method of motion control for formation is presented, which is based on the dynamic regulation and scheduling scheme. It is attractive for its adaptability to the formation structure and desired trajectory. The quality of formation keeping can be evaluated by the instantaneous errors of formation offset and spacing distance. Some kinematics laws are developed to regulate and maintain the formation shape. Simulation results and data analysis show the validity of the proposed approach for a group of robots.

Formation Control of Mobile Robots with Active Obstacle Avoidance

In this paper, the formation control and obstacle avoidance problems are dealt with a unified control algorithm, which allows the follower to avoid obstacle while maintaining desired relative bearing or relative distance from the leader. In the known leader-follower robot formation control literature, absolute motion states of the leader robot are required to control the followers, which may not be available in some environments. In this research, the leader-follower robot formation is modelled and controlled in terms of the relative motion states between the leader and follower robots. The absolute motion states of the leader robot are not required in the proposed formation controller. Furthermore, the research has been extended to a novel obstacle avoidance scheme based on sensing the relative motion between robot and obstacle. Experimental investigation has been conducted using the platform consisted of three nonholonomic mobile robots and computer vision system, and the results have demonstrated the effectiveness of the proposed methods.

Distributed Diagnosis in Formations of Mobile Robots

Multirobot systems are being increasingly used for a variety of tasks in manufacturing, surveillance, and space exploration. These systems can degrade or develop faults during operation, and, therefore, require online diagnosis algorithms to ensure safe operation. Centralized approaches to online diagnosis of robot formations do not scale well for two primary reasons: 1) the computational complexity of the algorithm grows significantly with the number of robots, and 2) the individual robots must communicate a large number of measurements to a central diagnoser. To overcome these problems, we present a distributed, model-based, qualitative fault-diagnosis approach for formations of mobile robots. The approach is based on a bond-graph modeling framework that can deal with multiple sensor types and isolate process, sensor, and actuator faults. The diagnosis scheme employs relative measurement orderings to discriminate among faults by exploiting the temporal order of measurement deviations. This increases the discriminatory power of the measurement set and produces a more efficient fault-isolation algorithm. We describe a distributed diagnoser design algorithm applied to robot formations. Experimental results demonstrate the improvement in both the discriminatory power of the measurements produced by the relative measurement orderings, and the computational efficiency achieved by the distributed-diagnosis approach

Coalition Formation: From Software Agents to Robots

A problem that has recently attracted the attention of the research community is the autonomous formation of robot teams to perform complex multi-robot tasks. The corresponding problem for software agents is also known in the multi-agent community as the coalition formation problem. Numerous algorithms for software agent coalition formation have been provided that allow for efficient cooperation in both competitive and cooperative environments. However, despite the plethora of relevant literature on the software agent coalition formation problem, and the existence of similar problems in theoretical computer science, the multi-robot coalition formation problem has not been sufficiently grounded for different tasks and task environments. In this paper, comparisons are drawn to highlight the differences between software agents and robotics, and parallel problems from theoretical computer science are identified. This paper further explores robot coalition formation in different practical robotic environments. A heuristic-based coalition formation algorithm from our previous work was extended to operate in precedence ordered cooperative environments. In order to explore coalition formation in competitive environments, the paper also studies the RACHNA system, a market based coalition formation system. Finally, the paper investigates the notion of task preemption for complex multi-robot tasks in random allocation environments.