Dynamically Stable 3D Quadrupedal Walking with Multi-Domain Hybrid System Models and Virtual Constraint Controllers

Hybrid systems theory has become a powerful approach for designing feedback controllers that achieve dynamically stable bipedal locomotion, both formally and in practice. This paper presents an analytical framework 1) to address multi-domain hybrid models of quadruped robots with high degrees of freedom, and 2) to systematically design nonlinear controllers that asymptotically stabilize periodic orbits of these sophisticated models. A family of parameterized virtual constraint controllers is proposed for continuous-time domains of quadruped locomotion to regulate holonomic and nonholonomic outputs. The properties of the Poincare return map for the full-order and closed-loop hybrid system are studied to investigate the asymptotic stabilization problem of dynamic gaits. An iterative optimization algorithm involving linear and bilinear matrix inequalities is then employed to choose stabilizing virtual constraint parameters. The paper numerically evaluates the analytical results on a simulation model of an advanced 3D quadruped robot, called GR Vision 60, with 36 state variables and 12 control inputs. An optimal amble gait of the robot is designed utilizing the FROST toolkit. The power of the analytical framework is finally illustrated through designing a set of stabilizing virtual constraint controllers with 180 controller parameters.Comment: American Control Conference 201

On Distributed Implementation of Switch-Based Adaptive Dynamic Programming

Switch-based adaptive dynamic programming (ADP) is an optimal control problem in which a cost must be minimized by switching among a family of dynamical modes. When the system dimension increases, the solution to switch-based ADP is made prohibitive by the exponentially increasing structure of the value function approximator and by the exponentially increasing modes. This technical correspondence proposes a distributed computational method for solving switch-based ADP. The method relies on partitioning the system into agents, each one dealing with a lower dimensional state and a few local modes. Each agent aims to minimize a local version of the global cost while avoiding that its local switching strategy has conflicts with the switching strategies of the neighboring agents. A heuristic algorithm based on the consensus dynamics and Nash equilibrium is proposed to avoid such conflicts. The effectiveness of the proposed method is verified via traffic and building test cases

Uniform finite time stabilisation of non-smooth and variable structure systems with resets

This thesis studies uniform finite time stabilisation of uncertain variable structure and non-smooth systems with resets. Control of unilaterally constrained systems is a challenging area that requires an understanding of the underlying mechanics that give rise to reset or jumps while synthesizing stabilizing controllers. Discontinuous systems with resets are studied in various disciplines. Resets in states are hard nonlinearities. This thesis bridges non-smooth Lyapunov analysis, the quasi-homogeneity of differential inclusions and uniform finite time stability for a class of impact mechanical systems. Robust control synthesis based on second order sliding mode is undertaken in the presence of both impacts with finite accumulation time and persisting disturbances. Unlike existing work described in the literature, the Lyapunov analysis does not depend on the jumps in the state while also establishing proofs of uniform finite time stability. Orbital stabilization of fully actuated mechanical systems is established in the case of persisting impacts with an a priori guarantee of finite time convergence between t he periodic impacts. The distinguishing features of second order sliding mode controllers are their simplicity and robustness. Increasing research interest in the area has been complemented by recent advances in Lyapullov based frameworks which highlight the finite time Convergence property. This thesis computes the upper bound on the finite settling time of a second order sliding mode controller. Different to the latest advances in the area, a key contribution of this thesis is the theoretical proof of the fact that finite settling time of a second order sliding mode controller tends to zero when gains tend to infinity. This insight of the limiting behaviour forms the basis for solving the converse problem of finding an explicit a priori tuning formula for the gain parameters of the controller when and arbitrary finite settling time is given. These results play a central role ill the analysis of impact mechanical systems. Another key contribution of the thesis is that it extends the above results on variable structure systems with and without resets to non-smooth systems arising from continuous finite time controllers while proving uniform finite time stability. Finally, two applications are presented. The first application applies the above theoretical developments to the problem of orbital stabilization of a fully actuated seven link biped robot which is a nonlinear system with periodic impacts. The tuning of the controller gains leads to finite time convergence of the tracking errors between impacts while being robust to disturbances. The second application reports the outcome of an experiment with a continuous finite time controller

Adjusting the parameters of the mechanical impedance for velocity, impact and force control

This work is dedicated to the analysis of the application of active impedance control for the realisation of three objectives simultaneously: velocity regulation in free motion, impact attenuation and finally force tracking. At first, a brief analysis of active impedance control is made, deducing the value of each parameter in order to achieve the three objectives. It is demonstrated that the system may be made overdamped with the adequate selection of the parameters if the characteristics of the environment are known, avoiding high overshoots of force during the impact. The second and most important contribution of this work is an additional measure for impact control in the case when the characteristics of the environment are unknown. It consists in switching among different values of the parameters of the impedance in order to dissipate faster the energy of the system, limiting the peaks of force and avoiding losses of contact. The optimal switching criteria are deduced for every parameter in order to dissipate the energy of the system as fast as possible. The results are verified in simulation. © 2011 Cambridge University Press.The authors want to express their gratitude to the Plan Nacional de I+D, Comision Interministerial de Ciencia y Tecnologia (FEDER-CICYT) for the partial financing of this work under the projects DPI2009-13830-C02-01 and DPI2010-20814-C02-02.Zotovic Stanisic, R.; Valera Fernández, Á. (2012). Adjusting the parameters of the mechanical impedance for velocity, impact and force control. Robotica. 30(4):10-25. doi:10.1017/S0263574711000725S1025304Siciliano, B., Sciavicco, L., Villani, L., & Oriolo, G. (2009). Robotics. Advanced Textbooks in Control and Signal Processing. doi:10.1007/978-1-84628-642-1Zotovic Stanisic, R., & Valera Fernández, Á. (2009). Simultaneous velocity, impact and force control. Robotica, 27(7), 1039-1048. doi:10.1017/s0263574709005451Seraji, H., & Colbaugh, R. (1997). Force Tracking in Impedance Control. The International Journal of Robotics Research, 16(1), 97-117. doi:10.1177/027836499701600107Hogan, N. (1985). Impedance Control: An Approach to Manipulation: Part I—Theory. Journal of Dynamic Systems, Measurement, and Control, 107(1), 1-7. doi:10.1115/1.3140702A nonlinear PD controller for force and contact transient control. (1995). IEEE Control Systems, 15(1), 15-21. doi:10.1109/37.341859Brogliato, B., Niculescu, S.-I., & Orhant, P. (1997). On the control of finite-dimensional mechanical systems with unilateral constraints. IEEE Transactions on Automatic Control, 42(2), 200-215. doi:10.1109/9.554400Tsuji, T., & Tanaka, Y. (2008). Bio-mimetic impedance control of robotic manipulator for dynamic contact tasks. Robotics and Autonomous Systems, 56(4), 306-316. doi:10.1016/j.robot.2007.09.001Impact modeling and control for industrial manipulators. (1998). IEEE Control Systems, 18(4), 65-71. doi:10.1109/37.710879Ott, C., Albu-Schaffer, A., Kugi, A., & Hirzinger, G. (2008). On the Passivity-Based Impedance Control of Flexible Joint Robots. IEEE Transactions on Robotics, 24(2), 416-429. doi:10.1109/tro.2008.915438Brogliato, B. (1999). Nonsmooth Mechanics. Communications and Control Engineering. doi:10.1007/978-1-4471-0557-2Edwards, C. (1998). Sliding Mode Control. doi:10.1201/9781498701822Armstrong, B. S. R., Gutierrez, J. A., Wade, B. A., & Joseph, R. (2006). Stability of Phase-Based Gain Modulation with Designer-Chosen Switch Functions. The International Journal of Robotics Research, 25(8), 781-796. doi:10.1177/0278364906067543Ziren Lu, & Goldenberg, A. A. (1995). Robust Impedance Control and Force Regulation: Theory and Experiments. The International Journal of Robotics Research, 14(3), 225-254. doi:10.1177/027836499501400303Controlling contact transition. (1994). IEEE Control Systems, 14(1), 25-30. doi:10.1109/37.257891Armstrong, B., Neevel, D., & Kusik, T. (2001). New results in NPID control: Tracking, integral control, friction compensation and experimental results. IEEE Transactions on Control Systems Technology, 9(2), 399-406. doi:10.1109/87.911392Volpe, R., & Khosla, P. (1993). A Theoretical and Experimental Investigation of Impact Control for Manipulators. The International Journal of Robotics Research, 12(4), 351-365. doi:10.1177/02783649930120040

Redesigning the human-robot interface : intuitive teleoperation of anthropomorphic robots

textA novel interface for robotic teleoperation was developed to enable accurate and highly efficient teleoperation of the Industrial Reconfigurable Anthropomorphic Dual-arm (IRAD) system and other robotic systems. In order to achieve a revolutionary increase in operator productivity, the bilateral/master-slave approach must give way to shared autonomy and unilateral control; autonomy must be employed where possible, and appropriate sensory feedback only where autonomy is impossible; and today’s low-information/high feedback model must be replaced by one that emphasizes feedforward precision and minimal corrective feedback. This is emphasized for task spaces outside of the traditional anthropomorphic scale such as mobile manipulation (i.e. large task spaces) and high precision tasks (i.e. very small task spaces). The system is demonstrated using an anthropomorphically dimensioned industrial manipulator working in task spaces from one meter to less than one millimeter, in both simulation and hardware. This thesis discusses the design requirements and philosophy of this interface, provides a summary of prototype teleoperation hardware, simulation environment, test-bed hardware, and experimental results.Mechanical Engineerin

Intelligent methods for complex systems control engineering

This thesis proposes an intelligent multiple-controller framework for complex systems that incorporates a fuzzy logic based switching and tuning supervisor along with a neural network based generalized learning model (GLM). The framework is designed for adaptive control of both Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) complex systems. The proposed methodology provides the designer with an automated choice of using either: a conventional Proportional-Integral-Derivative (PID) controller, or a PID structure based (simultaneous) Pole and Zero Placement controller. The switching decisions between the two nonlinear fixed structure controllers is made on the basis of the required performance measure using the fuzzy logic based supervisor operating at the highest level of the system. The fuzzy supervisor is also employed to tune the parameters of the multiple-controller online in order to achieve the desired system performance. The GLM for modelling complex systems assumes that the plant is represented by an equivalent model consisting of a linear time-varying sub-model plus a learning nonlinear sub-model based on Radial Basis Function (RBF) neural network. The proposed control design brings together the dominant advantages of PID controllers (such as simplicity in structure and implementation) and the desirable attributes of Pole and Zero Placement controllers (such as stable set-point tracking and ease of parameters’ tuning). Simulation experiments using real-world nonlinear SISO and MIMO plant models, including realistic nonlinear vehicle models, demonstrate the effectiveness of the intelligent multiple-controller with respect to tracking set-point changes, achieve desired speed of response, prevent system output overshooting and maintain minimum variance input and output signals, whilst penalising excessive control actions

Current-Mode Techniques for the Implementation of Continuous- and Discrete-Time Cellular Neural Networks

This paper presents a unified, comprehensive approach to the design of continuous-time (CT) and discrete-time (DT) cellular neural networks (CNN) using CMOS current-mode analog techniques. The net input signals are currents instead of voltages as presented in previous approaches, thus avoiding the need for current-to-voltage dedicated interfaces in image processing tasks with photosensor devices. Outputs may be either currents or voltages. Cell design relies on exploitation of current mirror properties for the efficient implementation of both linear and nonlinear analog operators. These cells are simpler and easier to design than those found in previously reported CT and DT-CNN devices. Basic design issues are covered, together with discussions on the influence of nonidealities and advanced circuit design issues as well as design for manufacturability considerations associated with statistical analysis. Three prototypes have been designed for l.6-pm n-well CMOS technologies. One is discrete-time and can be reconfigured via local logic for noise removal, feature extraction (borders and edges), shadow detection, hole filling, and connected component detection (CCD) on a rectangular grid with unity neighborhood radius. The other two prototypes are continuous-time and fixed template: one for CCD and other for noise removal. Experimental results are given illustrating performance of these prototypes