Multi-robot Formation Control With Limited Information Of Leader’s Velocity

Even since the last two decades, the multi-robot technology has been attractingwidespread attention, and people have done a lot of research in this area. Compared with asingle-robot system, a multi-robot system could achieve better performances in intelligence,robustness and adaptability. This paper discusses the problem of multiple autonomousmobile robots formation using local information, and mainly draws attention on how toimprove the capacity of attenuating disturbances of the system, and how to design propercontrollers using a limited or even totally no information of the leader robot’s velocity. Itdesigns some controllers to steer the follower robot to get into and maintain somepredesigned formation with the leader robot based on the leader-follower formationmethodology.Most of the existed researches of mobile robot formation control are mainly dealingwith how to design a formation controller under an idea environment, that all of theparameters needed for the controller can be detected or obtained directly. In order toenhance the usability for the algorithm and applicability for the robots, a more commonsituation should be considered for the algorithm design, such as the parameters neededcannot be detected directly according to the sensors. Furthermore, in order to reduce thedegree of coupling among robots, there should also consider how to reduce the dependencewith each other. All of these are not only the focal point but also the difficulty for the robotformation controller design. To deal with these cases, this dissertation starts with discussinghow to improve the system’s robustness and designing some controllers for the multi-robotsystem. Following, the controller design method via a situation that the follower robotcannot obtain part information of the leader robot’s velocity, and then to discuss thecontroller design method via a situation that the follower robot cannot obtain anyinformation of the leader robot’s velocity. Combining the controllers designed with theadaptive switching strategies, the obstacle avoidance and formation switching problems arediscussed for the formation system, and a good result is obtained. Finally, some experiments are provided to verify the effectiveness of the algorithms proposed. The wholediscussion is layer progressive and demonstrates an effective combination of theory andapplication.Firstly, this paper reviews the development and current research status of themulti-robot technology. Secondly, it introduces the dynamic model and control method of asingle robot system, and deduces the dynamic formation equations of a two-robot systembased on the distance-bearing model and a three-robot system based on thedistance-distance model according to the single robot’s dynamic equation.The dissertation is divided into two parts. The former part is the control algorithmdeduction and MATLAB simulation in theory, which mainly includes(1) Due to the fact that some uncertainties may occur in the formation system (such asdue to the sensor’s real position does not coincide with it’s expected position, which maycause some uncertainties), under the condition that the follower robot can obtain completeinformation of the leader robot (for both distance-bearing model and distance-distancemodel), a novel second order sliding mode control algorithm is proposed to improve theperformance of the standard sliding mode control method and to increase the controlaccuracy and restrain chatting phenomenon for the system. Under the condition that theuncertainties are satisfied some constraints, the system is driven to some assigned surfaceof the manifold and the formation tracking variables are forced to converge to their desiredvalues to obtain a desired formation along the manifold. The problem of obstacle avoidanceduring the follower robot tracking to the leader robot is discussed based on thedistance-distance formation model.(2) Under the condition that all information of the system is known or can be detected,it discusses the dynamic motion of the robot in a slipping situation, and deduces the relativeformation equations, that complements and delvelops the existed formation models.According to the compensation and merging methods, the dynamic formation equationsunder slipping condition are transformed into the style similar to the formation equationswithout slipping, and then the controller is designed similarly to the case without slipping. (3) Due to the sensor or transmission mechanism limitations, the assumption that thefollower robot can obtain complete information of the leader robot may not hold in somesituations. For this problem, it considers that the leader robot has a constant velocity, butthe follower robot cannot obtain this velocity in any away. The leader robot’s linear velocityis estimated dynamically by the adaptive output feedback method using relative positioninformation, and the estimated value is added into the controller designed. This algorithmreduces the requiment of paramets detecting via using and delveloping the advantagies ofboth of the input and out feedback algorithm and adptive algorithm. For this algorithm, thecontroller designed followers the procedures of the estimation design method. In order toenhance the flexibility for the controller design, the immersion and invariance algorithm isemployed to estimate the linear velocity of the leader robot, and the formation variables areobserved at the same time, at last the second order sliding mode control algorithm is chosento design a control law for the observed system, it achieves the objective of increasing thesystem robustness and decreasing the couping among the subparts simultaneously. Thedeficiency of needing a complete known paramets for the second order sliding mode controlmethodology is made up by the immersion and invariance based second order sliding modecontrol algorithm, and this algorithm is also an effective complement and updating for theimmersion and invariance algorithm.(4) Furthermore, in order to reduce the restrictions depending on the sensor’sperformance for the control algorithm, it considers that the follower robot has totally noinformation of the leader robot’s dynamic velocities, including linear velocity and angularvelocity. The traditional control error directly based algorithm is changed and upgraded inthis dissertation, and an adaptive formation algorithm is constructed for the formationsystem by conbinding the advantagies of the input and output linearization method. Firstly,an ideal controller is designed to satisfy the performance required. Secondly, the adaptiveformation control algorithm is used to approach the output of the ideal controller to obtainthe goal of forming a formation without knowing any information of the leader robot’svelocity. The adaptive gain parameters are adjusted according to the system’s performance dynamically. And the formation error can be reduced to small enough by selecting thecontrol parameters (the parameters excluding the adaptive gains) properly. The proposedcontroller does not need to estimate the leader robot’s velocity, and is rather simple andconvenient in realization.The latter part of this dissertation is the multi-robot formation experiments. Amulti-robot moving platform is set up based on the AmigoBot robots to check theeffectiveness of the theoretical algorithms running on the physical system, and each of theformation algorithms is verified and analyzed through the relative experiment. Theexperiment results validae the effectiveness of the algorithms proposed.Finally, some conclusions and prospects are given.