Mohamed W. Mehrez

Model Predictive Control of Nonholonomic Mobile Robots Without Stabilizing Constraints and Costs

The problem of steering a nonholonomic mobile robot to a desired position and orientation is considered. In this paper, a model predictive control (MPC) scheme based on tailored nonquadratic stage cost is proposed to fulfill this control task. We rigorously prove asymptotic stability while neither stabilizing constraints nor costs are used. To this end, we first design suitable maneuvers to construct bounds on the value function. Second, these bounds are exploited to determine a prediction horizon length such that the asymptotic stability of the MPC closed loop is guaranteed. Finally, numerical simulations are conducted to explain the necessity of having nonquadratic running costs.

An Optimization Based Approach for Relative Localization and Relative Tracking Control in Multi-Robot Systems

In this paper, an optimization based method is used for relative localization and relative trajectory tracking control in Multi-Robot Systems (MRS’s). In this framework, one or more robots are located and commanded to follow time varying trajectories with respect to another (possibly moving) robot reference frame. Such systems are suitable for a considerable number of applications, e.g. patrolling missions, searching operations, perimeter surveillance, and area coverage. Here, the nonlinear and constrained motion and measurement models in an MRS are incorporated to achieve an accurate state estimation algorithm based on nonlinear Moving Horizon Estimation (MHE) and a tracking control method based on Nonlinear Model Predictive Control (NMPC). In order to fulfill the real-time requirements, a fast and efficient algorithm based on a Real Time Iteration (RTI) scheme and automatic C-code generation, is adopted. Numerical simulations are conducted to: first, compare the performance of MHE against the traditional estimator used for relative localization, i.e. extended Kalman filter (EKF); second, evaluate the utilized relative localization and tracking control algorithm when applied to a team of multiple robots; finally, laboratory experiments are performed, for real-time performance evaluation. The conducted simulations validated the adopted algorithm and the experiments demonstrated its practical applicability.

Nonlinear moving horizon state estimation for multi-robot relative localization

This paper presents a novel approach for a multi-robot systems relative localization (RL), where one or more robots are located and tracked with respect to another robot frame of reference. With a known initial estimate of a robot being tracked, the extended Kalman filter (EKF) has been shown to perform adequately well to achieve the RL. However, with an arbitrary initial estimate, EKF performance may become unstable and/or require a high number of iterations to achieve an acceptable tracking error. In this paper, moving horizon estimation (MHE) has been adopted to achieve the RL objective. Although MHE has been highlighted in the literature to be computationally intractable, in this work, an efficient algorithm based on Real Time Iteration (RTI) scheme has been exported using an automatic C code generation toolkit. The exported code is adapted for the RL problem and requires computational capacity of the order ones of milliseconds. The MHE performance is compared against the EKF in numerical simulations. Under arbitrary estimator initialization, the results confirms that MHE over performs EKF in terms of the number of iterations required for convergence while satisfying the real-time requirements.

Differential communication with distributed MPC based on occupancy grid

Abstract We introduce a Distributed Model Predictive Control (DMPC) algorithm, which is based on the novel idea of projecting predicted trajectories on a quantised spatial set to reduce the communication load. The scheme exploits advantages of continuous optimisation methods while only quantised data is broadcasted. Further, we set up a differential communication scheme, in which only altered cells instead of the full prediction are broadcasted. While the quantisation reduces the communication effort for the overall system, the differential communication further reduces the effort depending on the chosen cell size. The approach is evaluated in simulations using groups of holonomic and non-holonomic mobile robots.

Interaction of open and closed loop control in MPC

Abstract We present a novel MPC algorithm without terminal constraints and/or costs, for which the prediction horizon is reduced in comparison to standard MPC while asymptotic stability and inherent robustness properties are maintained. To this end, we derive simplified stability conditions and investigate the interplay of open and closed loop control in MPC. The insight gained from this analysis allows to close the control loop more often while keeping the computational complexity of basic MPC. Our findings are verified by numerical simulations.