Adaptive IDA-PBC for underactuated mechanical systems with constant disturbances

This work investigates the control of nonlinear underactuated mechanical systems with matched and unmatched constant disturbances. To this end, a new control strategy is proposed, which builds upon the interconnection‐and‐damping‐assignment passivity‐based control, augmenting it with an additional term for the purpose of disturbance compensation. In particular, the disturbances are estimated adaptively and then accounted for in the control law employing a new matching condition of algebraic nature. Stability conditions are discussed, and for comparison purposes, an alternative controller based on partial feedback linearization is presented. The effectiveness of the proposed approach is demonstrated with numerical simulations for three motivating examples: the inertia wheel pendulum, the disk‐on‐disk system, and the pendulum‐on‐cart system

Design of an Adaptive Super-Twisting Control for the Cart-Pole Inverted Pendulum System

A cart-pole inverted pendulum system is one of the underactuated systems that has been used in many applications. This research aims to study the design and the effectiveness of the Adaptive Super-Twisting controller to stabilize the system by comparing it with other previous control methods. A stabilization control of the pendulum upright using the Adaptive Super-Twisting algorithm (ASTA), was investigated. The proposed controller was designed based on the decoupling algorithm method to solve the coupled control input in the system model. We then compared the proposed stabilizing controller with first-order sliding mode control (FOSMC) and Super-Twisting algorithm (STA) in Matlab/Simulink simulation and realistic computer simulation. We developed the computer simulation using anyKode Marilou software, which adopted Open-Dynamic Engine (ODE) as a physics engine. In Matlab/Simulink simulation, we considered three different scenarios: a nominal system, a system with uncertainty, and a disturbed system. Meanwhile, in a computer simulation, we only presented the comparison of different controllers' performances for the realized system. Both results showed that the three controllers could stabilize the pendulum upright with a 0.1 rad initial angular position around the vertical axis. Under the same conditions, the ASTA and STA controllers had similar performances; they both have less chattering and faster convergence than the FOSMC approach. However, the FOSMC approach had the least energy delivered and smallest errors than the other two approaches

ADAPTIVE WAVELETS SLIDING MODE CONTROL FOR A CLASS OF SECOND ORDER UNDERACTUATED MECHANICAL SYSTEMS

The control of underactuated mechanical systems (UMS) remains an attracting field where researchers can develop their control algorithms. To this date, various linear and nonlinear control techniques using classical and intelligent methods have been published in literature. In this work, an adaptive controller using sliding mode control (SMC) and wavelets network (WN) is proposed for a class of second-order UMS with two degrees of freedom (DOF).This adaptive control strategy takes advantage of both sliding mode control and wavelet properties. In the main result, we consider the case of un-modeled dynamics of the above-mentioned UMS, and we introduce a wavelets network to design an adaptive controller based on the SMC. The update algorithms are directly extracted by using the gradient descent method and conditions are then settled to achieve the required convergence performance.The efficacy of the proposed adaptive approach is demonstrated through an application to the pendubot

Sliding mode control trajectory tracking implementation on underactuated dynamic systems

Master of ScienceDepartment of Mechanical EngineeringWarren N. WhiteThe subject of linear control is a mature subject that has many proven powerful techniques. Recent research generally falls into the area of non-linear control. A subsection of non-linear control that has garnered a lot of research recently has been in underactuated dynamic systems. Many applications of the subject exist in robotics, aerospace, marine, constrained systems, walking systems, and non-holonomic systems. This thesis proposes a sliding mode control law for the tracking control of an underactuated dynamic system. A candidate Lyapunov function is used to build the desired tracking control. The proposed control method does not require the integration of feedback as does its predecessor. The proposed control can work on a variety of underactuated systems. Its predecessor only worked on those dynamic systems that are simply underactuated (torques acting on some joints, no torques acting on others). For dynamic systems that contain a roll without slip constraint, often a desired trajectory to follow is related to dynamic coordinates through a non-holonomic constraint. A navigational control is shown to work in conjunction with the sliding mode control to allow tracking of these desired trajectories. The methodology is applied through simulations to a holonomic case of the Segbot, an inverted cart-pole, a non-holonomic case of Segbot, and a rolling wheel. The methodology is implemented on an actual Segbot and shown to provide more favorable tracking results than linear feedback gains

Second order sliding mode control of underactuated Mechanical systems I: Local stabilization with application to an inverted pendulum

International audienceSecond order sliding mode control synthesis is developed for underactuated mechanical systems, operating under uncertainty conditions. In order to locally stabilize an underactuated system around an unstable equilibrium, an output is specified in such a way that the corresponding zero dynamics is locally asymptotically stable. Then, the desired stability property of the closed-loop system is provided by applying a quasihomogeneous second order sliding mode controller, driving the system to the zero dynamics manifold in finite time. Although the present synthesis exhibits an infinite number of switches on a finite time interval, it does not rely on the generation of first order sliding modes, while providing robustness features similar to those possessed by their standard sliding mode counterparts. A second order sliding mode appears on the zero dynamics manifold which is of co-dimension greater than the control space dimension. Performance issues of the proposed synthesis are illustrated in numerical and experimental studies of a cart-Pendulum system

Data-Driven Passivity-Based Control of Underactuated Robotic Systems

Classical control strategies for robotic systems are based on the idea that feedback control can be used to override the natural dynamics of the machines. Passivity-based control (Pbc) is a branch of nonlinear control theory that follows a similar approach, where the natural dynamics is modified based on the overall energy of the system. This method involves transforming a nonlinear control system, through a suitable control input, into another fictitious system that has desirable stability characteristics. The majority of Pbc techniques require the discovery of a reasonable storage function, which acts as a Lyapunov function candidate that can be used to certify stability. There are several challenges in the design of a suitable storage function, including: 1) what a reasonable choice for the function is for a given control system, and 2) the control synthesis requires a closed-form solution to a set of nonlinear partial differential equations. The latter is in general difficult to overcome, especially for systems with high degrees of freedom, limiting the applicability of Pbc techniques. A machine learning framework that automatically determines the storage function for underactuated robotic systems is introduced in this dissertation. This framework combines the expressive power of neural networks with the systematic methods of the Pbc paradigm, bridging the gap between controllers derived from learning algorithms and nonlinear control theory. A series of experiments demonstrates the efficacy and applicability of this framework for a family of underactuated robots

A two-wheeled machine with a handling mechanism in two different directions

Despite the fact that there are various configurations of self-balanced two-wheeled machines (TWMs), the workspace of such systems is restricted by their current configurations and designs. In this work, the dynamic analysis of a novel configuration of TWMs is introduced that enables handling a payload attached to the intermediate body (IB) in two mutually perpendicular directions. This configuration will enlarge the workspace of the vehicle and increase its flexibility in material handling, objects assembly and similar industrial and service robot applications. The proposed configuration gains advantages of the design of serial arms while occupying a minimum space which is unique feature of TWMs. The proposed machine has five degrees of freedoms (DOFs) that can be useful for industrial applications such as pick and place, material handling and packaging. This machine will provide an advantage over other TWMs in terms of the wider workspace and the increased flexibility in service and industrial applications. Furthermore, the proposed design will add additional challenge of controlling the system to compensate for the change of the location of the COM due to performing tasks of handling in multiple directions

Modeling and Control Strategies for a Two-Wheel Balancing Mobile Robot

The problem of balancing and autonomously navigating a two-wheel mobile robot is an increasingly active area of research, due to its potential applications in last-mile delivery, pedestrian transportation, warehouse automation, parts supply, agriculture, surveillance, and monitoring. This thesis investigates the design and control of a two-wheel balancing mobile robot using three different control strategies: Proportional Integral Derivative (PID) controllers, Sliding Mode Control, and Deep Q-Learning methodology. The mobile robot is modeled using a dynamic and kinematic model, and its motion is simulated in a custom MATLAB/Simulink environment. The first part of the thesis focuses on developing a dynamic and kinematic model for the mobile robot. The robot dynamics is derived using the classical Euler-Lagrange method, where motion can be described using potential and kinetic energies of the bodies. Non-holonomic constraints are included in the model to achieve desired motion, such as non-drifting of the mobile robot. These non-holonomic constraints are included using the method of Lagrange multipliers. Navigation for the robot is developed using artificial potential field path planning to generate a map of velocity vectors that are used for the set points for linear velocity and yaw rate. The second part of the thesis focuses on developing and evaluating three different control strategies for the mobile robot: PID controllers, Hierarchical Sliding Mode Control, and Deep-Q-Learning. The performances of the different control strategies are evaluated and compared based on various metrics, such as stability, robustness to mass variations and disturbances, and tracking accuracy. The implementation and evaluation of these strategies are modeled tested in a MATLAB/SIMULINK virtual environment

Modeling and Control Strategies for a Two-Wheel Balancing Mobile Robot

The problem of balancing and autonomously navigating a two-wheel mobile robot is an increasingly active area of research, due to its potential applications in last-mile delivery, pedestrian transportation, warehouse automation, parts supply, agriculture, surveillance, and monitoring. This thesis investigates the design and control of a two-wheel balancing mobile robot using three different control strategies: Proportional Integral Derivative (PID) controllers, Sliding Mode Control, and Deep Q-Learning methodology. The mobile robot is modeled using a dynamic and kinematic model, and its motion is simulated in a custom MATLAB/Simulink environment. The first part of the thesis focuses on developing a dynamic and kinematic model for the mobile robot. The robot dynamics is derived using the classical Euler-Lagrange method, where motion can be described using potential and kinetic energies of the bodies. Non-holonomic constraints are included in the model to achieve desired motion, such as non-drifting of the mobile robot. These non-holonomic constraints are included using the method of Lagrange multipliers. Navigation for the robot is developed using artificial potential field path planning to generate a map of velocity vectors that are used for the set points for linear velocity and yaw rate. The second part of the thesis focuses on developing and evaluating three different control strategies for the mobile robot: PID controllers, Hierarchical Sliding Mode Control, and Deep-Q-Learning. The performances of the different control strategies are evaluated and compared based on various metrics, such as stability, robustness to mass variations and disturbances, and tracking accuracy. The implementation and evaluation of these strategies are modeled tested in a MATLAB/SIMULINK virtual environment