Control Of Nonh=holonomic Systems

Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic systems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization problem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic autonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles\u27 kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveillance and formation control of a group of nonholonomic robots is investigated. A designing scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs

Coordinated Control of a Mobile Manipulator

In this technical report, we investigate modeling, control, and coordination of mobile manipulators. A mobile manipulator in this study consists of a robotic manipulator and a mobile platform, with the manipulator being mounted atop the mobile platform. A mobile manipulator combines the dextrous manipulation capability offered by fixed-base manipulators and the mobility offered by mobile platforms. While mobile manipulators offer a tremendous potential for flexible material handling and other tasks, at the same time they bring about a number of challenging issues rather than simply increasing the structural complexity. First, combining a manipulator and a platform creates redundancy. Second, a wheeled mobile platform is subject to nonholonomic constraints. Third, there exists dynamic interaction between the manipulator and the mobile platform. Fourth, manipulators and mobile platforms have different bandwidths. Mobile platforms typically have slower dynamic response than manipulators. The objective of the thesis is to develop control algorithms that effectively coordinate manipulation and mobility of mobile manipulators. We begin with deriving the motion equations of mobile manipulators. The derivation presented here makes use of the existing motion equations of manipulators and mobile platforms, and simply introduces the velocity and acceleration dependent terms that account for the dynamic interaction between manipulators and mobile platforms. Since nonholonomic constraints play a critical role in control of mobile manipulators, we then study the control properties of nonholonomic dynamic systems, including feedback linearization and internal dynamics. Based on the newly proposed concept of preferred operating region, we develop a set of coordination algorithms for mobile manipulators. While the manipulator performs manipulation tasks, the mobile platform is controlled to always bring the configuration of the manipulator into a preferred operating region. The control algorithms for two types of tasks - dragging motion and following motion - are discussed in detail. The effects of dynamic interaction are also investigated. To verify the efficacy of the coordination algorithms, we conduct numerical simulations with representative task trajectories. Additionally, the control algorithms for the dragging motion and following motion have been implemented on an experimental mobile manipulator. The results from the simulation and experiment are presented to support the proposed control algorithms

Analysis of multi-agent systems under varying degrees of trust, cooperation, and competition

Multi-agent systems rely heavily on coordination and cooperation to achieve a variety of tasks. It is often assumed that these agents will be fully cooperative, or have reliable and equal performance among group members. Instead, we consider cooperation as a spectrum of possible interactions, ranging from performance variations within the group to adversarial agents. This thesis examines several scenarios where cooperation and performance are not guaranteed. Potential applications include sensor coverage, emergency response, wildlife management, tracking, and surveillance. We use geometric methods, such as Voronoi tessellations, for design insight and Lyapunov-based stability theory to analyze our proposed controllers. Performance is verified through simulations and experiments on a variety of ground and aerial robotic platforms. First, we consider the problem of Voronoi-based coverage control, where a group of robots must spread out over an environment to provide coverage. Our approach adapts online to sensing and actuation performance variations with the group. The robots have no prior knowledge of their relative performance, and in a distributed fashion, compensate by assigning weaker robots a smaller portion of the environment. Next, we consider the problem of multi-agent herding, akin to shepherding. Here, a group of dog-like robots must drive a herd of non-cooperative sheep-like agents around the environment. Our key insight in designing the control laws for the herders is to enforce geometrical relationships that allow for the combined system dynamics to reduce to a single nonholonomic vehicle. We also investigate the cooperative pursuit of an evader by a group of quadrotors in an environment with no-fly zones. While the pursuers cannot enter the no-fly zones, the evader moves freely through the zones to avoid capture. Using tools for Voronoi-based coverage control, we provide an algorithm to distribute the pursuers around the zone's boundary and minimize capture time once the evader emerges. Finally, we present an algorithm for the guaranteed capture of multiple evaders by one or more pursuers in a bounded, convex environment. The pursuers utilize properties of the evader's Voronoi cell to choose a control strategy that minimizes the safe-reachable area of the evader, which in turn leads to the evader's capture

Park City Lectures on Mechanics, Dynamics, and Symmetry

In these ve lectures, I cover selected items from the following topics: 1. Reduction theory for mechanical systems with symmetry, 2. Stability, bifurcation and underwater vehicle dynamics, 3. Systems with rolling constraints and locomotion, 4. Optimal control and stabilization of balance systems, 5. Variational integrators. Each topic itself could be expanded into several lectures, but I limited myself to what I could reasonably explain in the allotted time. The hope is that the overview is informative enough so that the reader can understand the fundamental ideas and can intelligently choose from the literature for additional details on topics of interest. Compatible with the theme of the PCI graduate school, I assume that the readers are familiar with the elements of geometric mechanics, including the basics of symplectic and Poisson geometry. The reader can find the needed background in, for example, Marsden and Ratiu [1998]

A Framework for Scalable Cooperative Navigation of Autonomous Vehicles

We describe a general framework for controlling and coordinating a group of non-holonomic mobile robots equipped with range sensors, with applications ranging from scouting and reconnaissance, to search and rescue and manipulation tasks. We first describe a set of control laws that allows each robot to control its position and orientation with respect to neighboring robots or obstacles in the environment. We then develop a coordination protocol that allows the robots to automatically switch between the control laws to follow a specified trajectory. Finally, we describe two simple trajectory generators that are derived from potential field theory. The first allows each robot to plan its reference trajectory based on the information available to it. The second scheme requires sharing of information and results in a trajectory for the designated leader. Numerical simulations illustrate the application of these ideas and demonstrate the scalability of the proposed framework for a large group of robots

Exponential Stabilization of Driftless Nonlinear Control Systems

This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form, xdot = X1(x)u1 + .... + Xm(x)um, x ∈ ℝ^n Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineering applications it is often required to maintain the mechanical system around a desired configuration. This task is treated as a stabilization problem where the desired configuration is made an asymptotically stable equilibrium point. The control design is carried out on an approximate system. The approximation process yields a nilpotent set of input vector fields which, in a special coordinate system, are homogeneous with respect to a non-standard dilation. Even though the approximation can be given a coordinate-free interpretation, the homogeneous structure is useful to exploit: the feedbacks are required to be homogeneous functions and thus preserve the homogeneous structure in the closed-loop system. The stability achieved is called p-exponential stability. The closed-loop system is stable and the equilibrium point is exponentially attractive. This extended notion of exponential stability is required since the feedback, and hence the closed-loop system, is not Lipschitz. However, it is shown that the convergence rate of a Lipschitz closed-loop driftless system cannot be bounded by an exponential envelope. The synthesis methods generate feedbacks which are smooth on ℝ^n \ {0}. The solutions of the closed-loop system are proven to be unique in this case. In addition, the control inputs for many driftless systems are velocities. For this class of systems it is more appropriate for the control law to specify actuator forces instead of velocities. We have extended the kinematic velocity controllers to controllers which command forces and still p-exponentially stabilize the system. Perhaps the ultimate justification of the methods proposed in this thesis are the experimental results. The experiments demonstrate the superior convergence performance of the p-exponential stabilizers versus traditional smooth feedbacks. The experiments also highlight the importance of transformation conditioning in the feedbacks. Other design issues, such as scaling the measured states to eliminate hunting, are discussed. The methods in this thesis bring the practical control of strongly nonlinear systems one step closer