Dynamics and Control of Higher-order Nonholonomic Systems

A theoretical framework is established for the control of higher-order nonholonomic systems, defined as systems that satisfy higher-order nonintegrable constraints. A model for such systems is developed in terms of differential-algebraic equations defined on a higher-order tangent bundle. A number of control-theoretic properties such as nonintegrability, controllability, and stabilizability are presented. Higher-order nonholonomic systems are shown to be strongly accessible and, under certain conditions, small time locally controllable at any equilibrium. There are important examples of higher-order nonholonomic systems that are asymptotically stabilizable via smooth feedback, including space vehicles with multiple slosh modes and Prismatic-Prismatic-Revolute (PPR) robots moving open liquid containers, as well as an interesting class of systems that do not admit asymptotically stabilizing continuous static or dynamic state feedback. Specific assumptions are introduced to define this class, which includes important examples of robotic systems. A discontinuous nonlinear feedback control algorithm is developed to steer any initial state to the equilibrium at the origin. The applicability of the theoretical development is illustrated through two examples: control of a planar PPR robot manipulator subject to a jerk constraint and control of a point mass moving on a constant torsion curve in a three dimensional space

Stabilization of cascaded nonlinear systems under sampling and delays

Over the last decades, the methodologies of dynamical systems and control theory have been playing an increasingly relevant role in a lot of situations of practical interest. Though, a lot of theoretical problem still remain unsolved. Among all, the ones concerning stability and stabilization are of paramount importance. In order to stabilize a physical (or not) system, it is necessary to acquire and interpret heterogeneous information on its behavior in order to correctly intervene on it. In general, those information are not available through a continuous flow but are provided in a synchronous or asynchronous way. This issue has to be unavoidably taken into account for the design of the control action. In a very natural way, all those heterogeneities define an hybrid system characterized by both continuous and discrete dynamics. This thesis is contextualized in this framework and aimed at proposing new methodologies for the stabilization of sampled-data nonlinear systems with focus toward the stabilization of cascade dynamics. In doing so, we shall propose a small number of tools for constructing sampled-data feedback laws stabilizing the origin of sampled-data nonlinear systems admitting cascade interconnection representations. To this end, we shall investigate on the effect of sampling on the properties of the continuous-time system while enhancing design procedures requiring no extra assumptions over the sampled-data equivalent model. Finally, we shall show the way sampling positively affects nonlinear retarded dynamics affected by a fixed and known time-delay over the input signal by enforcing on the implicit cascade representation the sampling process induces onto the retarded system

Large scale dynamic systems

Classes of large scale dynamic systems were discussed in the context of modern control theory. Specific examples discussed were in the technical fields of aeronautics, water resources and electric power

A Survey of path following control strategies for UAVs focused on quadrotors

The trajectory control problem, defined as making a vehicle follow a pre-established path in space, can be solved by means of trajectory tracking or path following. In the trajectory tracking problem a timed reference position is tracked. The path following approach removes any time dependence of the problem, resulting in many advantages on the control performance and design. An exhaustive review of path following algorithms applied to quadrotor vehicles has been carried out, the most relevant are studied in this paper. Then, four of these algorithms have been implemented and compared in a quadrotor simulation platform: Backstepping and Feedback Linearisation control-oriented algorithms and NLGL and Carrot-Chasing geometric algorithms.Peer ReviewedPostprint (author's final draft

Rigid Body Attitude Estimation: An Overview and Comparative Study

The attitude estimation of rigid body systems has attracted the attention of many researchers over the years. The development of efficient estimation algorithms that can accurately estimate the orientation of a rigid body is a crucial step towards a reliable implementation of control schemes for underwater and flying vehicles. The primary focus of this thesis consists in investigating various attitude estimation techniques and their applications. Two major classes are discussed. The first class consists of the earliest static attitude determination techniques relying solely on a set of body vector measurements of known vectors in the inertial frame. The second class consists of dynamic attitude estimation and filtering techniques, relying on body vector measurements as well other measurements, and using the dynamical equations of the system under consideration. Various attitude estimation algorithms, including the latest nonlinear attitude observers, are presented and discussed, providing a survey that covers the evolution and structural differences of these estimation methods. Simulation results have been carried out for a selected number of such attitude estimators. Their performance in the presence of noisy measurements, as well as their advantages and disadvantages are discussed

Spacecraft nonlinear attitude control with bounded control input

The research in this thesis deals with nonlinear control of spacecraft attitude stabilization and tracking manoeuvres and addresses the issue of control toque saturation on a priori basis. The cascaded structure of spacecraft attitude kinematics and dynamics makes the method of integrator backstepping preferred scheme for the spacecraft nonlinear attitude control. However, the conventional backstepping control design method may result in excessive control torque beyond the saturation bound of the actuators. While remaining within the framework of conventional backstepping control design, the present work proposes the formulation of analytical bounds for the control torque components as functions of the initial attitude and angular velocity errors and the gains involved in the control design procedure. The said analytical bounds have been shown to be useful for tuning the gains in a way that the guaranteed maximum torque upper bound lies within the capability of the actuator and, hence, addressing the issue of control input saturation. Conditions have also been developed as well as the generalization of the said analytical bounds which allow for the tuning of the control gains to guarantee prescribed stability with the additional aim that the control action avoids reaching saturation while anticipating the presence of bounded external disturbance torque and uncertainties in the spacecraft moments of inertia. Moreover, the work has also been extended blending it with the artificial potential function method for achieving autonomous capability of avoiding pointing constraints for the case of spacecraft large angle slew manoeuvres. The idea of undergoing such manoeuvres using control moment gyros to track commanded angular momentum rather than a torque command has also been studied. In this context, a gimbal position command generation algorithm has been proposed for a pyramid-type cluster of four single gimbal control moment gyros. The proposed algorithm not only avoids the saturation of the angular momentum input from the control moment gyro cluster but also exploits its maximum value deliverable by the cluster along the direction of the commanded angular momentum for the major part of the manoeuvre. In this way, it results in rapid spacecraft slew manoeuvres. The ideas proposed in the thesis have also been validated using numerical simulations and compared with results already existing in the literature