Optimization based solutions for control and state estimation in non-holonomic mobile robots: stability, distributed control, and relative localization

Interest in designing, manufacturing, and using autonomous robots has been rapidly growing during the most recent decade. The main motivation for this interest is the wide range of potential applications these autonomous systems can serve in. The applications include, but are not limited to, area coverage, patrolling missions, perimeter surveillance, search and rescue missions, and situational awareness. In this thesis, the area of control and state estimation in non-holonomic mobile robots is tackled. Herein, optimization based solutions for control and state estimation are designed, analyzed, and implemented to such systems. One of the main motivations for considering such solutions is their ability of handling constrained and nonlinear systems such as non-holonomic mobile robots. Moreover, the recent developments in dynamic optimization algorithms as well as in computer processing facilitated the real-time implementation of such optimization based methods in embedded computer systems. Two control problems of a single non-holonomic mobile robot are considered first; these control problems are point stabilization (regulation) and path-following. Here, a model predictive control (MPC) scheme is used to fulfill these control tasks. More precisely, a special class of MPC is considered in which terminal constraints and costs are avoided. Such constraints and costs are traditionally used in the literature to guarantee the asymptotic stability of the closed loop system. In contrast, we use a recently developed stability criterion in which the closed loop asymptotic stability can be guaranteed by appropriately choosing the prediction horizon length of the MPC controller. This method is based on finite time controllability as well as bounds on the MPC value function. Afterwards, a regulation control of a multi-robot system (MRS) is considered. In this control problem, the objective is to stabilize a group of mobile robots to form a pattern. We achieve this task using a distributed model predictive control (DMPC) scheme based on a novel communication approach between the subsystems. This newly introduced method is based on the quantization of the robots’ operating region. Therefore, the proposed communication technique allows for exchanging data in the form of integers instead of floating-point numbers. Additionally, we introduce a differential communication scheme to achieve a further reduction in the communication load. Finally, a moving horizon estimation (MHE) design for the relative state estimation (relative localization) in an MRS is developed in this thesis. In this framework, robots with less payload/computational capacity, in a given MRS, are localized and tracked using robots fitted with high-accuracy sensory/computational means. More precisely, relative measurements between these two classes of robots are used to localize the less (computationally) powerful robotic members. As a complementary part of this study, the MHE localization scheme is combined with a centralized MPC controller to provide an algorithm capable of localizing and controlling an MRS based only on relative sensory measurements. The validity and the practicality of this algorithm are assessed by realtime laboratory experiments. The conducted study fills important gaps in the application area of autonomous navigation especially those associated with optimization based solutions. Both theoretical as well as practical contributions have been introduced in this research work. Moreover, this thesis constructs a foundation for using MPC without stabilizing constraints or costs in the area of non-holonomic mobile robots