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Unified Modeling Approach of Kinematics, Dynamics and Control of a Free-Flying Space Robot Interacting with a Target Satellite  [PDF]
Murad Shibli
Intelligent Control and Automation (ICA) , 2011, DOI: 10.4236/ica.2011.21002
Abstract: In this paper a unified control-oriented modeling approach is proposed to deal with the kinematics, linear and angular momentum, contact constraints and dynamics of a free-flying space robot interacting with a target satellite. This developed approach combines the dynamics of both systems in one structure along with holonomic and nonholonomic constraints in a single framework. Furthermore, this modeling allows consid-ering the generalized contact forces between the space robot end-effecter and the target satellite as internal forces rather than external forces. As a result of this approach, linear and angular momentum will form holonomic and nonholonomic constraints, respectively. Meanwhile, restricting the motion of the space robot end-effector on the surface of the target satellite will impose geometric constraints. The proposed momentum of the combined system under consideration is a generalization of the momentum model of a free-flying space robot. Based on this unified model, three reduced models are developed. The first reduced dynamics can be considered as a generalization of a free-flying robot without contact with a target satellite. In this re-duced model it is found that the Jacobian and inertia matrices can be considered as an extension of those of a free-flying space robot. Since control of the base attitude rather than its translation is preferred in certain cases, a second reduced model is obtained by eliminating the base linear motion dynamics. For the purpose of the controller development, a third reduced-order dynamical model is then obtained by finding a common solution of all constraints using the concept of orthogonal projection matrices. The objective of this approach is to design a controller to track motion trajectory while regulating the force interaction between the space robot and the target satellite. Many space missions can benefit from such a modeling system, for example, autonomous docking of satellites, rescuing satellites, and satellite servicing, where it is vital to limit the con-tact force during the robotic operation. Moreover, Inverse dynamics and adaptive inverse dynamics control-lers are designed to achieve the control objectives. Both controllers are found to be effective to meet the specifications and to overcome the un-actuation of the target satellite. Finally, simulation is demonstrated by to verify the analytical results.
Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints  [PDF]
Melvin Leok,Tomoki Ohsawa,Diana Sosa
Mathematics , 2011, DOI: 10.1063/1.4736733
Abstract: We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton-Jacobi equation as the Dirac-Hamilton-Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the theory specializes to the recently developed nonholonomic Hamilton-Jacobi theory. We are particularly interested in applications to a certain class of degenerate nonholonomic Lagrangian systems with symmetries, which we refer to as weakly degenerate Chaplygin systems, that arise as simplified models of nonholonomic mechanical systems; these systems are shown to reduce to non-degenerate almost Hamiltonian systems, i.e., generalized Hamiltonian systems defined with non-closed two-forms. Accordingly, the Dirac-Hamilton-Jacobi equation reduces to a variant of the nonholonomic Hamilton-Jacobi equation associated with the reduced system. We illustrate through a few examples how the Dirac-Hamilton-Jacobi equation can be used to exactly integrate the equations of motion.
Tethered Flying Robot for Information Gathering System  [PDF]
Tohru Ishii,Yasutake Takahashi,Yoichiro Maeda,Takayuki Nakamura
Computer Science , 2013,
Abstract: Information from the sky is important for rescue activity in large-scale disaster or dangerous areas. Observation system using a balloon or an airplane has been studied as an information gathering system from the sky. A balloon observation system needs helium gas and relatively long time to be ready. An airplane observation system can be prepared in a short time and its mobility is good. However, a long time flight is difficult because of limited amount of fuel. This paper proposes a kite-based observation system that complements activities of balloon and airplane observation systems by short preparation time and long time flight. This research aims at construction of the autonomous flight information gathering system using a tethered flying unit that consists of the kite and the ground tether line control unit with a winding machine. This paper reports development of the kite type tethered flying robot and an autonomous flying control system inspired by how to fly a kite by a human.
Simulator for Control of Autonomous Nonholonomic Wheeled Mobile Robot
Tang Howe Hing,Musa Mailah
Journal of Applied Sciences , 2008,
Abstract: The study presents a Virtual Reality (VR) technique that is used in the construction of a nonholonomic Wheeled Mobile Robot (WMR) simulator for the experimentation of robotic control algorithms. The modelling of the proposed simulator involves motion planning, motion control and the application of a VR technique that employ a number of strategies and algorithms. The role of a trajectory planner as the interface mechanism between the motion planner and controller is particularly highlighted to facilitate the overall design of the simulator. The interlinking between the main components is also relevantly described prior to the execution of a simulation study that takes into account a number of operating and loading conditions. A case study includes the application of different control schemes to the WMR that is executing a tracking task with disturbances applied at its actuators in a virtual Computer Integrated Manufacturing (CIM) environment. Results of the study indicate the effectiveness of the proposed simulator in demonstrating the WMR capability to manoeuvre desirably towards its target destination while at the same time avoiding the collision with obstacles along its travelled path.
An Adaptive Control Scheme for Nonholonomic Mobile Robot with Parametric Uncertainty
F. Mnif,F. Touati
International Journal of Advanced Robotic Systems , 2008,
Abstract: This paper addresses the problem of stabilizing the dynamic model of a nonholonomic mobile robot. A discontinuous adaptive state feedback controller is derived to achieve global stability and convergence of the trajectories of the of the closed loop system in the presence of parameter modeling uncertainty. This task is achieved by a non smooth transformation in the original system followed by the derivation of a smooth time invariant control in the new coordinates. The stability and convergence analysis is built on Lyapunov stability theory.
Adaptive Tracking Control of an Uncertain Nonholonomic Robot  [PDF]
Nan Hu, Chaoli Wang
Intelligent Control and Automation (ICA) , 2011, DOI: 10.4236/ica.2011.24045
Abstract: In this paper, a new controller is proposed by using backstepping method for the trajectory tracking problem of nonholonomic dynamic mobile robots with nonholonomic constraints under the condition that there is a distance between the mass center and the geometrical center and the distance is unknown. And an adaptive feedback controller is also proposed for the case that some kinematic parameters and dynamic parameters are uncertain. The asymptotical stability of the control system is proved with Lyapunov stability theory. The simulation results show the effectiveness of the proposed controller. The comparison with the previous methods is made to show the effectiveness of the method in this article.
Energy Reduction with Anticontrol of Chaos for Nonholonomic Mobile Robot System
Zahra Yaghoubi,Hassan Zarabadipour,Mahdi Aliyari Shoorehdeli
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/854140
Abstract: This paper presents energy reduction with anticontrol of chaos for nonholonomic mobile robot system. Anticontrol of chaos is also called chaotification, meaning to chaotify an originally non-chaotic system, and in this paper error of mobile robot system has been synchronized with chaotic gyroscope for reducing energy and increasing performance. The benefits of chaos synchronization with mechanical systems have led us to an innovation in this paper. The main purpose is that the control system in the presence of chaos work with lower control cost and control effort has been reduced. For comparison of proposed method, the feedback linearization controller has also been designed for mobile robot with noise. Finally, the efficacies of the proposed method have been illustrated by simulations, energy of control signals has been calculated, and effect of Alpha (: a constant coefficient is used beside of chaotic system) variations on the energy of control signals has been checked.
Trajectory Planning for Nonholonomic Mobile Robot Using Extended Kalman Filter  [PDF]
Leonimer Flavio de Melo,Jose Fernando Mangili Junior
Mathematical Problems in Engineering , 2010, DOI: 10.1155/2010/979205
Abstract: In the mobile robotic systems, a precise estimate of the robot pose with the intention of the optimization in the path planning is essential for the correct performance, on the part of the robots, for tasks that are destined to it. This paper describes the use of RF digital signal interacting with beacons for computational triangulation in the way to provide a pose estimative at bidimensional indoor environment, where GPS system is out of range. This methodology takes advantage of high-performance multicore DSP processors to calculate ToF of the order about ns. Sensors data like odometry, compass, and the result of triangulation Cartesian estimative, are fused for better position estimative. It uses a mathematical and computational tool for nonlinear systems with time-discrete sampling for pose estimative calculation of mobile robots, with the utilization of extended Kalman filter (EKF). A mobile robot platform with differential drive and nonholonomic constraints is used as a base for state space, plants and measurements models that are used in the simulations and validation of the experiments. 1. Introduction The planning of trajectory for the mobile robots, and consequently its better estimative of positioning, is the reason of intense scientific inquiry. A good path planning of trajectory is fundamental for optimization of the interrelation between the environment and the mobile robot. A great diversity of techniques based on different physical principles exists and different algorithms for the localization and the planning of the best possible trajectory. The localization in structuralized environment is helped, in general, by external elements that are called of markers. It is possible to use natural markers that already existing in the environment for the localization. Another possibility is to add intensionally to the environment artificial markers to guide the localization of the robot. This work uses an important mathematical and computational tool for the calculation of the data fusing collected by the sensors and the disturbances caused for the errors, with the purpose of estimate the mobile robot pose, that is the Extended Kalman filter (EKF). A mobile robot platform with differential traction and nonholonomics restrictions is used for experiments validation. In the direct kinematics the system of mobile robot positioning is presented. A model for state space, plants and measurements are presented, that are needed for the development of the necessary attributes to the positioning estimates made with the Extended Kalman filter. Finally, we
On Robust Hybrid Force/Motion Control Strategies Based on Actuator Dynamics for Nonholonomic Mobile Manipulators
Yongxin Zhu,Liping Fan
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/920260
Abstract: Robust force/motion control strategies are presented for mobile manipulators under both holonomic and nonholonomic constraints in the presence of uncertainties and disturbances. The controls are based on structural knowledge of the dynamics of the robot, and the actuator dynamics is also taken into account. The proposed control is robust not only to structured uncertainty such as mass variation but also to unstructured one such as disturbances. The system stability and the boundness of tracking errors are proved using Lyapunov stability theory. The proposed control strategies guarantee that the system motion converges to the desired manifold with prescribed performance. Simulation results validate that not only the states of the system asymptotically converge to the desired trajectory, but also the constraint force asymptotically converges to the desired force.
Finite-Time Stabilization of Stochastic Nonholonomic Systems and Its Applicationto Mobile Robot
Fangzheng Gao,Fushun Yuan
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/361269
Abstract: This paper investigates the problem of finite-time stabilization for a class of stochastic nonholonomic systems in chained form. By using stochastic finite-time stability theorem and the method of adding a power integrator, a recursive controller design procedure in the stochastic setting is developed. Based on switching strategy to overcome the uncontrollability problem associated with , global stochastic finite-time regulation of the closed-loop system states is achieved. The proposed scheme can be applied to the finite-time control of nonholonomic mobile robot subject to stochastic disturbances. The simulation results demonstrate the validity of the presented algorithm.
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