Dynamics, Directional Maneuverability and Optimization Based Multivariable Control of Nonholonomic Differential Drive Mobile Robots

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).