Abstract-Cooperative manipulation, where several robots collaboratively transport an object, poses a great challenge in robotics. In order to avoid object deformations in cooperative manipulation, formation rigidity of the robots is desired. This work proposes a novel linear state feedback controller that combines both optimal goal regulation and a relaxed form of the formation rigidity constraint, exploiting an underlying distributed impedance control scheme. Since the presented control design problem is in a biquadratic LQR-like form, we present an iterative design algorithm to compute the controller. As an intermediate result, an approximated state-space model of an interconnected robot system is derived. The controller design approach is evaluated in a full-scale multi-robot experiment.

Distributed control of large-scale dynamical systems poses a new challenge to the field of control driven by the technological advances of modern communication networks. A particular challenge is the distributed design of such control systems. Here, a distributed iterative controller synthesis method for continuous time linear systems using a gradient descent method is presented. One of the main contributions is the determination of the step size according to a distributed BarzilaiBorwein (BB) method. As the control objective, we treat the finite horizon linear quadratic cost functional. The gradient approach uses communication only with direct neighbors and is based on the forward simulation of the system states and the backwards simulation of adjoint states. The effectiveness of the approach is shown by means of numerical simulations.

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Privacy concerns spark the desire to analyze largescale interconnected systems in a distributed fashion, i.e. without a central entity having global model knowledge. Two different approaches are presented to analyze stability of interconnected linear time-invariant systems with limited model knowledge. The two algorithms implement sufficient stability conditions and require information exchange only with direct neighbors thus reducing the need to share model data widely and ensuring privacy. The first algorithm is based on an M-matrix condition, the second one on Lyapunov inequalities. Both algorithms rely on distributed optimization using a dual decomposition approach. Numerical investigations are used to validate both approaches.

Abstract-Cooperative manipulation of multiple robots presents an interesting control application scenario of coupled dynamical systems with a common goal. Here, we treat the problem of moving a formation of physically interconnected robots to a desired goal while maintaining the formation. This control problen is for example relevant in cooperative transport of an object from an initial to a final configuration by mobile robotic manipulators. To achieve the control goal we formulate an LQR-like optimal control problem that, in addition to goal regulation and minimization of input energy, includes the formation rigidity constraint in a relaxed form expressed as a biquadratic penalty term. The control problem is solved by two different iterative algorithms, a gradient descent using adjoint states and a quasi-Newton method, that determine a static linear state-feedback matrix. The proposed control design and the iterative algorithms are validated and compared in numerical simulations showing the efficacy of both approaches.