Derivative-Free Distributed Filtering for MIMO Robotic Systems under Delays and Packet Drops

This paper presents an approach to distributed state estimation-based control of nonlinear MIMO systems, capable of incorporating delayed measurements in the estimation algorithm while also being robust to packet losses. First, the paper examines the problem of distributed nonlinear filtering over a communication/sensors network, and the use of the estimated state vector in a control loop. As a possible filtering approach, an extended information filter (EIF) is proposed. The extended information filter requires the computation of Jacobians which in the case of high order nonlinear dynamical systems can be a cumbersome procedure, while it also introduces cumulative errors to the state estimation due to the approximative linearization performed in the Taylor series expansion of the system's nonlinear model. To overcome the aforementioned weaknesses of the extended information filter, a derivative-free approach to extended information filtering has been proposed. Distributed filtering is now based on a derivative-free implementation of Kalman filtering which is shown to be applicable to MIMO nonlinear dynamical systems. In the proposed derivative-free extended information filtering, the system is first subject to a linearization transformation that makes use of the differential flatness theory. It is shown how the proposed distributed filtering method can succeed in compensation of random delays and packet drops which may appear during the transmission of measurements and of state vector estimates, thus assuring a reliable performance of the distributed filtering-based control scheme. Evaluation tests are carried out on benchmark MIMO nonlinear systems, such as multi-DOF robotic manipulators.