This dissertation presents a comprehensive study of modeling and control issues associated with nonholonomic differential drive mobile robots. The first part of dissertation focuses on modeling using Lagrangian mechanics. The dynamics is modeled as a two-input two-output (TITO) nonlinear model. Motor dynamics are also modeled. Trade studies are conducted to shed light on critical vehicle design parameters, and how they impact static properties, dynamic properties, directional stability, coupling and overall vehicle design. An aspect ratio based dynamic decoupling condition is also presented. The second part of dissertation addresses design of linear time-invariant (LTI), multi-input multi-ouput (MIMO) fixed-structure H∞ controllers for the inner-loop velocity (v, ω) tracking system of the robot, motivated by a practical desire to design classically structured robust controllers. The fixed-structure H∞-optimal controllers are designed using Generalized Mixed Sensitivity(GMS) methodology to systematically shape properties at distinct loop breaking points. The H∞-control problem is solved using nonsmooth optimization techniques to compute locally optimal solutions. Matlab’s Robust Control toolbox (Hinfstruct and Systune) is used to solve the nonsmooth optimization. The dissertation also addresses the design of fixed-structure MIMO gain-scheduled H∞ controllers via GMS methodology. Trade-off studies are conducted to address the effect of vehicle design parameters on frequency and time domain properties of the inner-loop control system of mobile robot. The third part of dissertation focuses on the design of outer-loop position (x, y, θ) control system of mobile robot using real-time model predictive control (MPC) algorithms. Both linear time-varying (LTV) MPC and nonlinear MPC algorithms are discussed.The outer-loop performance of mobile robot is studied for two applications - 1) single robot trajectory tracking and multi-robot coordination in presence of obstacles, 2) maximum progress maneuvering on racetrack. The dissertation specifically addresses the impact of variation of c.g. position w.r.t. wheel-axle on directional maneuverability, peak control effort required to perform aggressive maneuvers, and overall position control performance. Detailed control relevant performance trade-offs associated with outer-loop position control are demonstrated through simulations in discrete time. Optimizations packages CPLEX(convex-QP in LTV-MPC) and ACADO(NLP in nonlinear-MPC) are used to solve the OCP in real time. All simulations are performed on Robot Operating System (ROS).

Mobile robots are used in a broad range of application areas; e.g. search and rescue, reconnaissance, exploration, etc. Given the increasing need for high performance mobile robots, the area has received attention by researchers. In this thesis, critical control and control-relevant design issues for differential drive mobile robots is addressed. Two major themes that have been explored are the use of kinematic models for control design and the use of decentralized proportional plus integral (PI) control. While these topics have received much attention, there still remain critical questions which have not been rigorously addressed. In this thesis, answers to the following critical questions are provided: When is 1. a kinematic model sufficient for control design? 2. coupled dynamics essential? 3. a decentralized PI inner loop velocity controller sufficient? 4. centralized multiple-input multiple-output (MIMO) control essential? and how can one design the robot to relax the requirements implied in 1 and 2? In this thesis, the following is shown: 1. The nonlinear kinematic model will suffice for control design when the inner velocity (dynamic) loop is much faster (10X) than the slower outer positioning loop. 2. A dynamic model is essential when the inner velocity (dynamic) loop is less than two times faster than the slower outer positioning loop. 3. A decentralized inner loop PI velocity controller will be sufficient for accomplish- ing high performance control when the required velocity bandwidth is small, rel- ative to the peak dynamic coupling frequency. A rule-of-thumb which depends on the robot aspect ratio is given. 4. A centralized MIMO velocity controller is needed when the required bandwidth is large, relative to the peak dynamic coupling frequency. Here, the analysis in the thesis is sparse making the topic an area for future analytical work. Despite this, it is clearly shown that a centralized MIMO inner loop controller can offer increased performance vis- ́a-vis a decentralized PI controller. 5. Finally, it is shown how the dynamic coupling depends on the robot aspect ratio and how the coupling can be significantly reduced. As such, this can be used to ease the requirements imposed by 2 and 4 above.