The power dissipation method and kinematic reducibility of multiple-model robotic systems

This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems

Dynamic modeling, property investigation, and adaptive controller design of serial robotic manipulators modeled with structural compliance

Research results on general serial robotic manipulators modeled with structural compliances are presented. Two compliant manipulator modeling approaches, distributed and lumped parameter models, are used in this study. System dynamic equations for both compliant models are derived by using the first and second order influence coefficients. Also, the properties of compliant manipulator system dynamics are investigated. One of the properties, which is defined as inaccessibility of vibratory modes, is shown to display a distinct character associated with compliant manipulators. This property indicates the impact of robot geometry on the control of structural oscillations. Example studies are provided to illustrate the physical interpretation of inaccessibility of vibratory modes. Two types of controllers are designed for compliant manipulators modeled by either lumped or distributed parameter techniques. In order to maintain the generality of the results, neither linearization is introduced. Example simulations are given to demonstrate the controller performance. The second type controller is also built for general serial robot arms and is adaptive in nature which can estimate uncertain payload parameters on-line and simultaneously maintain trajectory tracking properties. The relation between manipulator motion tracking capability and convergence of parameter estimation properties is discussed through example case studies. The effect of control input update delays on adaptive controller performance is also studied

Model reduction of synchronized homogeneous Lur'e networks with incrementally sector-bounded nonlinearities

This paper proposes a model order reduction scheme that reduces the complexity of diffusively coupled homogeneous Lur'e systems. We aim to reduce the dimension of each subsystem and meanwhile preserve the synchronization property of the overall network. Using the Laplacian spectral radius, we characterize the robust synchronization of the Lur'e network by a linear matrix inequality (LMI), whose solutions then are treated as generalized Gramians for the balanced truncation of the linear component of each Lur'e subsystem. It is verified that, with the same communication topology, the resulting reduced-order network system is still robustly synchronized, and an a priori bound on the approximation error is guaranteed to compare the behaviors of the full-order and reduced-order Lur'e subsystems

Model Reduction Methods for Complex Network Systems

Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of interconnections may also be of high complexity. Therefore, it is relevant to study reduction methods for network systems. An overview on reduction methods for both the topological (interconnection) structure of the network and the dynamics of the nodes, while preserving structural properties of the network, and taking a control systems perspective, is provided. First topological complexity reduction methods based on graph clustering and aggregation are reviewed, producing a reduced-order network model. Second, reduction of the nodal dynamics is considered by using extensions of classical methods, while preserving the stability and synchronization properties. Finally, a structure-preserving generalized balancing method for simplifying simultaneously the topological structure and the order of the nodal dynamics is treated.Comment: To be published in Annual Review of Control, Robotics, and Autonomous System

Mechanical Design, Modelling and Control of a Novel Aerial Manipulator

In this paper a novel aerial manipulation system is proposed. The mechanical structure of the system, the number of thrusters and their geometry will be derived from technical optimization problems. The aforementioned problems are defined by taking into consideration the desired actuation forces and torques applied to the end-effector of the system. The framework of the proposed system is designed in a CAD Package in order to evaluate the system parameter values. Following this, the kinematic and dynamic models are developed and an adaptive backstepping controller is designed aiming to control the exact position and orientation of the end-effector in the Cartesian space. Finally, the performance of the system is demonstrated through a simulation study, where a manipulation task scenario is investigated.Comment: Comments: 8 Pages, 2015 IEEE International Conference on Robotics and Automation (ICRA '15), Seattle, WA, US