Dynamic Control of Mobile Multirobot Systems: The Cluster Space Formulation

The formation control technique called cluster space control promotes simplified specification and monitoring of the motion of mobile multirobot systems of limited size. Previous paper has established the conceptual foundation of this approach and has experimentally verified and validated its use for various systems implementing kinematic controllers. In this paper, we briefly review the definition of the cluster space framework and introduce a new cluster space dynamic model. This model represents the dynamics of the formation as a whole as a function of the dynamics of the member robots. Given this model, generalized cluster space forces can be applied to the formation, and a Jacobian transpose controller can be implemented to transform cluster space compensation forces into robot-level forces to be applied to the robots in the formation. Then, a nonlinear model-based partition controller is proposed. This controller cancels out the formation dynamics and effectively decouples the cluster space variables. Computer simulations and experimental results using three autonomous surface vessels and four land rovers show the effectiveness of the approach. Finally, sensitivity to errors in the estimation of cluster model parameters is analyzed.Fil: Mas, Ignacio Agustin. Instituto Tecnológico de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Kitts, Christopher. Santa Clara University; Estados Unido

Geometric path planning without maneuvers for nonholonomic parallel orienting robots

Current geometric path planners for nonholonomic parallel orienting robots generate maneuvers consisting of a sequence of moves connected by zero-velocity points. The need for these maneuvers restrains the use of this kind of parallel robots to few applications. Based on a rather old result on linear time-varying systems, this letter shows that there are infinitely differentiable paths connecting two arbitrary points in SO(3) such that the instantaneous axis of rotation along the path rest on a fixed plane. This theoretical result leads to a practical path planner for nonholonomic parallel orienting robots that generates single-move maneuvers. To present this result, we start with a path planner based on three-move maneuvers, and then we proceed by progressively reducing the number of moves to one, thus providing a unified treatment with respect to previous geometric path planners.Peer ReviewedPostprint (author's final draft

Multirobot heterogeneous control considering secondary objectives

Cooperative robotics has considered tasks that are executed frequently, maintaining the shape and orientation of robotic systems when they fulfill a common objective, without taking advantage of the redundancy that the robotic group could present. This paper presents a proposal for controlling a group of terrestrial robots with heterogeneous characteristics, considering primary and secondary tasks thus that the group complies with the following of a path while modifying its shape and orientation at any time. The development of the proposal is achieved through the use of controllers based on linear algebra, propounding a low computational cost and high scalability algorithm. Likewise, the stability of the controller is analyzed to know the required features that have to be met by the control constants, that is, the correct values. Finally, experimental results are shown with di erent configurations and heterogeneous robots, where the graphics corroborate the expected operation of the proposalThis research was funded by Corporación Ecuatoriana para el Desarrollo de la Investigación y Academia–CEDI

Hybrid Controller based on Null Space and Consensus Algorithms for Mobile Robot Formation

This work presents a novel hybrid control approach based on null space and consensus algorithms to solve the scalability problems of mobile robot formation and improve leader control through multiple control objectives. In previous works, the training of robots based on the null space requires a rigid training structure based on a geometric shape, which increases the number of agents in the formation. The scheme of the control algorithm, which does not make formation scalability possible, must be changed; therefore, seeking the scalability of training based on null space is a challenge that could be solved with the inclusion of consensus algorithms, which allow the control structure to be maintained despite increasing or decreasing the number of robot followers. Another advantage of this proposal is that the formation of the followers does not depend on any geometric figure compared to previous works based on the null space; this new proposal does not present singularities as if the structure is based on geometric shape, the latter one is crucial since the formation of agents can take forms that cannot be achieved with a geometric structure, such as collinear locations, that can occur in many environments. The proposed hybrid control approach presents three tasks: i) leader position task, ii) leader shape task, and iii) follower formation task. The proposed algorithm is validated through simulations, performing tests that use the kinematic model of non-holonomic mobile robots. In addition, linear algebra and Lyapunov theory are used to analyze the stability of the method. Doi: 10.28991/ESJ-2022-06-03-01 Full Text: PD

Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control

Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they are not energy-preserving they do exhibit long-time stable energy behavior. However, variational integrators often simulate mechanical system dynamics by solving an implicit difference equation at each time step, one that is moreover expressed purely in terms of configurations at different time steps. This paper formulates the first- and second-order linearizations of a variational integrator in a manner that is amenable to control analysis and synthesis, creating a bridge between existing analysis and optimal control tools for discrete dynamic systems and variational integrators for mechanical systems in generalized coordinates with forcing and holonomic constraints. The forced pendulum is used to illustrate the technique. A second example solves the discrete LQR problem to find a locally stabilizing controller for a 40 DOF system with 6 constraints.Comment: 13 page

Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control

Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they are not energy-preserving they do exhibit long-time stable energy behavior. However, variational integrators often simulate mechanical system dynamics by solving an implicit difference equation at each time step, one that is moreover expressed purely in terms of configurations at different time steps. This paper formulates the first- and second-order linearizations of a variational integrator in a manner that is amenable to control analysis and synthesis, creating a bridge between existing analysis and optimal control tools for discrete dynamic systems and variational integrators for mechanical systems in generalized coordinates with forcing and holonomic constraints. The forced pendulum is used to illustrate the technique. A second example solves the discrete LQR problem to find a locally stabilizing controller for a 40 DOF system with 6 constraints.Comment: 13 page