Designing the Adaptive Tracking Controller for Uncertain Fully Actuated Dynamical Systems with Additive Disturbances Based on Sliding Mode

This paper addresses the problem of adaptive tracking control for uncertain fully actuated dynamical systems with additive disturbance (FDSA) based on the sliding mode. We use the adaptive mechanism to adjust the uncertain parameters in sliding mode control law which can be switched to two modes depending on the sliding surface. By choosing appropriately the parameters in control law, the desired transient time can be obtained without effects of uncertain parameters and additive disturbances. The chattering phenomenon can be minimized by a chosen constant. This control method is applied to the angles tracking control of the twin rotor multi-input multi-output system (TRMS) which have nonlinear characteristics, the input torque disturbances and the coupling between the horizontal and vertical movements. The simulation and experimental results are presented that validate the proposed solution

On Using Exponential Parameter Estimators with an Adaptive Controller

Typical adaptive controllers are restricted to using a specific update law to generate parameter estimates. This paper investigates the possibility of using any exponential parameter estimator with an adaptive controller such that the system tracks a desired trajectory. The goal is to provide flexibility in choosing any update law suitable for a given application. The development relies on a previously developed concept of controller/update law modularity in the adaptive control literature, and the use of a converse Lyapunov-like theorem. Stability analysis is presented to derive gain conditions under which this is possible, and inferences are made about the tracking error performance. The development is based on a class of Euler-Lagrange systems that are used to model various engineering systems including space robots and manipulators

Differentiable Robust Model Predictive Control

Deterministic model predictive control (MPC), while powerful, is often insufficient for effectively controlling autonomous systems in the real-world. Factors such as environmental noise and model error can cause deviations from the expected nominal performance. Robust MPC algorithms aim to bridge this gap between deterministic and uncertain control. However, these methods are often excessively difficult to tune for robustness due to the nonlinear and non-intuitive effects that controller parameters have on performance. To address this challenge, a unifying perspective on differentiable optimization for control is presented, which enables derivation of a general, differentiable tube-based MPC algorithm. The proposed approach facilitates the automatic and real-time tuning of robust controllers in the presence of large uncertainties and disturbances

Udwadia-Kalaba Approach for Three Link Manipulator Dynamics With Motion Constraints

Aiming to dynamic modeling of a three-link manipulator subjected to motion constraints, a novel explicit approach to the dynamical equations based on Udwadia-Kalaba (UK) theory is established. The motion constraints on the three-link manipulator can be regarded as external constraints of the system. However, it is not easy to obtain explicit equations for the dynamic modeling of constrained systems. For a multibody system subjecting to motion constraints, it is common to introduce Lagrange multipliers, but obtaining an explicit dynamical equation using traditional Lagrange multipliers is difficult. In order to obtain such equations more simply, motion constraints are handled using the UK equation. Compared with the Lagrange method, the UK approach can simplify the analysis and solution of a constrained system, without the need to introduce additional auxiliary variables to solve the Lagrange equation. Based on a more real-life nominal system (whose parameters are known) model considering the uncertain environment, this paper develops a nonlinear controller that satisfies the required trajectory. This controller allows the nonlinear nominal system to track the desired trajectory exactly without linearizations or approximations. These continuous controllers compensate extra force to eliminate the errors caused by uncertainties. The controllers are based on a generalization of sliding surfaces. Error bounds on tracking caused by uncertainties are analytically obtained. The numerical results show the simplicity and efficacy of the proposed methodology, and the reliability of the error bounds

Adaptive and Optimal Motion Control of Multi-UAV Systems

This thesis studies trajectory tracking and coordination control problems for single and multi unmanned aerial vehicle (UAV) systems. These control problems are addressed for both quadrotor and fixed-wing UAV cases. Despite the fact that the literature has some approaches for both problems, most of the previous studies have implementation challenges on real-time systems. In this thesis, we use a hierarchical modular approach where the high-level coordination and formation control tasks are separated from low-level individual UAV motion control tasks. This separation helps efficient and systematic optimal control synthesis robust to effects of nonlinearities, uncertainties and external disturbances at both levels, independently. The modular two-level control structure is convenient in extending single-UAV motion control design to coordination control of multi-UAV systems. Therefore, we examine single quadrotor UAV trajectory tracking problems to develop advanced controllers compensating effects of nonlinearities and uncertainties, and improving robustness and optimality for tracking performance. At fi rst, a novel adaptive linear quadratic tracking (ALQT) scheme is developed for stabilization and optimal attitude control of the quadrotor UAV system. In the implementation, the proposed scheme is integrated with Kalman based reliable attitude estimators, which compensate measurement noises. Next, in order to guarantee prescribed transient and steady-state tracking performances, we have designed a novel backstepping based adaptive controller that is robust to effects of underactuated dynamics, nonlinearities and model uncertainties, e.g., inertial and rotational drag uncertainties. The tracking performance is guaranteed to utilize a prescribed performance bound (PPB) based error transformation. In the coordination control of multi-UAV systems, following the two-level control structure, at high-level, we design a distributed hierarchical (leader-follower) 3D formation control scheme. Then, the low-level control design is based on the optimal and adaptive control designs performed for each quadrotor UAV separately. As particular approaches, we design an adaptive mixing controller (AMC) to improve robustness to varying parametric uncertainties and an adaptive linear quadratic controller (ALQC). Lastly, for planar motion, especially for constant altitude flight of fixed-wing UAVs, in 2D, a distributed hierarchical (leader-follower) formation control scheme at the high-level and a linear quadratic tracking (LQT) scheme at the low-level are developed for tracking and formation control problems of the fixed-wing UAV systems to examine the non-holonomic motion case. The proposed control methods are tested via simulations and experiments on a multi-quadrotor UAV system testbed

Control of Nonlinear Mechatronic Systems

This dissertation is divided into four self-contained chapters. In Chapter 1, an adaptive nonlinear tracking controller for kinematically redundant robot manipulators is presented. Past research efforts have focused on the end-effector tracking control of redundant robots because of their increased dexterity over their non-redundant counterparts. This work utilizes an adaptive full-state feedback quaternion based controller developed in [1] and focuses on the design of a general sub-task controller. This sub-task controller does not affect the position and orientation tracking control objectives, but instead projects a preference on the configuration of the manipulator based on sub-task objectives such as the following: singularity avoidance, joint limit avoidance, bounding the impact forces, and bounding the potential energy. In Chapter 2, two controllers are developed for nonlinear haptic and teleoperator systems for coordination of the master and slave systems. The first controller is proven to yield a semi-global asymptotic result in the presence of parametric uncertainty in the master and the slave dynamic models provided the user and the environmental input forces are measurable. The second controller yields a global asymptotic result despite unmeasurable user and environmental input forces provided the dynamic models of the master and slave systems are known. These controllers rely on a transformation and a flexible target system to allow the master system\u27s impedance to be easily adjusted so that it matches a desired target system. This work also offers a structure to encode a velocity field assist mechanism to provide the user help in controlling the slave system in completing a pre-defined contour following task. For each controller, Lyapunov-based techniques are used to prove that both controllers provide passive coordination of the haptic/teleoperator system when the velocity field assist mechanism is disabled. When the velocity field assist mechanism is enabled, the analysis proves the coordination of the haptic/teleoperator system. Simulation results are presented for both controllers. In Chapter 3, two controllers are developed for flat multi-input/multi-output nonlinear systems. First, a robust adaptive controller is proposed and proven to yield semi-global asymptotic tracking in the presence of additive disturbances and parametric uncertainty. In addition to guaranteeing an asymptotic output tracking result, it is also proven that the parameter estimate vector is driven to a constant vector. In the second part of the chapter, a learning controller is designed and proven to yield a semi-global asymptotic tracking result in the presence of additive disturbances where the desired trajectory is periodic. A continuous nonlinear integral feedback component is utilized in the design of both controllers and Lyapunov-based techniques are used to guarantee that the tracking error is asymptotically driven to zero. Numerical simulation results are presented for both controllers. In Chapter 4, a new dynamic model for continuum robot manipulators is derived. The dynamic model is developed based on the geometric model of extensible continuum robot manipulators with no torsional effects. The development presented in this chapter is an extension of the dynamic model proposed in [2] (by Mochiyama and Suzuki) to include a class of extensible continuum robot manipulators. First, the kinetic energy of a slice of the continuum robot is evaluated. Next, the total kinetic energy of the manipulator is obtained by utilizing a limit operation (i.e., sum of the kinetic energy of all the slices). Then, the gravitational potential energy of the manipulator is derived. Next, the elastic potential energy of the manipulator is derived for both bending and extension. Finally, the dynamic model of a planar 3-section extensible continuum robot manipulator is derived by utilizing the Lagrange representation. Numerical simulation results are presented for a planar 3-section extensible continuum robot manipulator