On the robustness of the slotine-Li and the FPT/SVD-based adaptive controllers

A comparative study concerning the robustness of a novel, Fixed Point Transformations/Singular Value Decomposition (FPT/SVD)-based adaptive controller and the Slotine-Li (S&L) approach is given by numerical simulations using a three degree of freedom paradigm of typical Classical Mechanical systems, the cart + double pendulum. The effects of the imprecision of the available dynamical model, presence of dynamic friction at the axles of the drives, and the existence of external disturbance forces unknown and not modeled by the controller are considered. While the Slotine-Li approach tries to identify the parameters of the formally precise, available analytical model of the controlled system with the implicit assumption that the generalized forces are precisely known, the novel one makes do with a very rough, affine form and a formally more precise approximate model of that system, and uses temporal observations of its desired vs. realized responses. Furthermore, it does not assume the lack of unknown perturbations caused either by internal friction and/or external disturbances. Its another advantage is that it needs the execution of the SVD as a relatively time-consuming operation on a grid of a rough system-model only one time, before the commencement of the control cycle within which it works only with simple computations. The simulation examples exemplify the superiority of the FPT/SVD-based control that otherwise has the deficiency that it can get out of the region of its convergence. Therefore its design and use needs preliminary simulation investigations. However, the simulations also exemplify that its convergence can be guaranteed for various practical purposes

Cooperative Object Manipulation with Force Tracking on the da Vinci Research Kit

The da Vinci Surgical System is one of the most established robot-assisted surgery device commended for its dexterity and ergonomics in minimally invasive surgery. Conversely, it inherits disadvantages which are lack of autonomy and haptic feedback. In order to address these issues, this work proposes an industry-inspired solution to the field of force control in medical robotics. This approach contributes to shared autonomy by developing a controller for cooperative object manipulation with force tracking utilizing available manipulators and force feedback. To achieve simultaneous position and force tracking of the object, master and slave manipulators were assigned then controlled with Cartesian position control and impedance control respectively. Because impedance control requires a model-based feedforward compensation, we identified the lumped base parameters of mass, inertias, and frictions of a three degree-of-freedom double four-bar linkage mechanism with least squares and weighted least squares regression methods. Additionally, semidefinite programming was used to constrain the parameters to a feasible physical solution in standard parameter space. Robust stick-slip static friction compensation was applied where linear Viscous and Coulomb friction was inadequate in modeling the prismatic third joint. The Robot Operating System based controller was tested in RViz to check the cooperative kinematics of up to three manipulators. Additionally, simulation with the dynamic engine Gazebo verified the cooperative controller applying a constant tension force on a massless spring-damper virtual object. With adequate model feedback linearization, the cooperative impedance controller tested on the da Vinci Research Kit yielded stable tension force tracking while simultaneously moving in Cartesian space. The maximum force tracking error was +/- 0.5 N for both a compliant and stiff manipulated object

System analysis, modelling and control with polytopic linear models

This research investigates the suitability of Polytopic Linear Models (PLMs) for the analysis, modelling and control of a class of nonlinear dynamical systems. The PLM structure is introduced as an approximate and alternative description of nonlinear dynamical systems for the benefit of system analysis and controller design. The model structure possesses three properties that we would like to exploit. Firstly, a PLM is build upon a number of linear models, each one of which describes the system locally within a so-called operating regime. If these models are combined in an appropriate way, that is by taking operating point dependent convex combinations of parameter values that belong to the different linear models, then a PLM will result. Consequently, the parameter values of a PLM vary within a polytope, and the vertices of this polytope are the parameter values that belong to the different linear models. A PLM owes its name to this feature. Accordingly, a PLM can be interpreted on the basis of a regime decomposition. Secondly, since a PLM is based on several linear models, it is possible to describe the nonlinear system more globally compared to only a single linear model. Thirdly, it is demonstrated that, under the appropriate conditions, nonlinear systems can be approximated arbitrary close by a PLM, parametrized with a finite number of parameters. There will be given an upper bound for the number of required parameters, that is sufficient to achieve the prescribed desired accuracy of the approximation. An important motivation for considering PLMs rests on its structural similarities with linear models. Linear systems are well understood, and the accompanying system and control theory is well developed. Whether or not the control related system properties such as stability, controllability etcetera, are fulfilled, can be demonstrated by means of (often relatively simple) mathematical manipulations on the linear system’s parameterization. Controller design can often be automated and founded on the parameterization and the control objective. Think of control laws based on stability, optimality and so on. For nonlinear systems this is only partly the case, and therefore further development of system and control theory is of major importance. In view of the similarities between a linear model and a PLM, the expectation exists that one can benefit from (results and concepts of) the well developed linear system and control theory. This hypothesis is partly confirmed by the results of this study. Under the appropriate conditions, and through a simple analysis of the parametrization of a PLM, it is possible to establish from a control perspective relevant system properties. One of these properties is stability. Under the appropriate conditions stability of the PLM implies stability of the system. Moreover, a few easy to check conditions are derived concerning the notion of controllability and observability. It has to be noticed however, that these conditions apply to a class of PLMs of which the structure is further restricted. The determination of system properties from a PLM is done with the intention to derive a suitable model, and in particular to design a model based controller. This study describes several constructive methods that aim at building a PLM representation of the real system. On the basis of a PLM several control laws are formulated. The main objective of these control laws is to stabilize the system in a desired operating point. A few computerized stabilizing control designs, that additionally aim at optimality or robustness, are the outcome of this research. The entire route of representing a system with an approximate PLM, subsequently analyzing the PLM, and finally controlling the system by a PLM based control design is illustrated by means of several examples. These examples include experimental as well as simulation studies, and nonlinear dynamic (mechanical) systems are the subject of research

A Novel Approach for Simplification of Industrial Robot Dynamic Model Using Interval Method

This paper proposes a new approach to simplify the dynamic model of industrial robot by means of interval method. Due to strong nonlinearities, some components of robot dynamic model such as the inertia matrix and the vector of centrifugal, Coriolis and gravitational torques, are very complicated for real-time control of industrial robots. Thus, a simplification algorithm is presented in this study in order to reduce the computation time and memory occupation. More importantly, this simplification is suitable for arbitrary trajectories in whole robot workspace. Furthermore, the method devotes to finding negligible inertia parameters, which is useful for robot model identification. A simulation has been carried out on a test trajectory using a 6-DOF industrial robot model, and the results have shown good performance and effectiveness of this method.ANR COROUSS

Robust Whole-Body Motion Control of Legged Robots

We introduce a robust control architecture for the whole-body motion control of torque controlled robots with arms and legs. The method is based on the robust control of contact forces in order to track a planned Center of Mass trajectory. Its appeal lies in the ability to guarantee robust stability and performance despite rigid body model mismatch, actuator dynamics, delays, contact surface stiffness, and unobserved ground profiles. Furthermore, we introduce a task space decomposition approach which removes the coupling effects between contact force controller and the other non-contact controllers. Finally, we verify our control performance on a quadruped robot and compare its performance to a standard inverse dynamics approach on hardware.Comment: 8 Page

Brachiating power line inspection robot: controller design and implementation

The prevalence of electrical transmission networks has led to an increase in productivity and prosperity. In 2014, estimates showed that the global electric power transmission network consisted of 5.5 million circuit kilometres (Ckm) of high-voltage transmission lines with a combined capacity of 17 million mega-volt ampere. The vastness of the global transmission grid presents a significant problem for infrastructure maintenance. The high maintenance costs, coupled with challenging terrain, provide an opportunity for autonomous inspection robots. The Brachiating Power Line Inspection Robot (BPLIR) with wheels [73] is a transmission line inspection robot. The BPLIR is the focus of this research and this dissertation tackles the problem of state estimation, adaptive trajectory generation and robust control for the BPLIR. A kinematics-based Kalman Filter state estimator was designed and implemented to determine the full system state. Instrumentation used for measurement consisted of 2 Inertial Measurement Units (IMUs). The advantages of utilising IMUs is that they are less susceptible to drift, have no moving parts and are not prone to misalignment errors. The use of IMU's in the design meant that absolute angles (link angles measured with respect to earth) could be estimated, enabling the BPLIR to navigate inclined slopes. Quantitative Feedback Control theory was employed to address the issue of parameter uncertainty during operation. The operating environment of the BPLIR requires it to be robust to environmental factors such as wind disturbance and uncertainty in joint friction over time. The resulting robust control system was able to compensate for uncertain system parameters and reject disturbances in simulation. An online trajectory generator (OTG), inspired by Raibert-style reverse-time symmetry[10], fed into the control system to drive the end effector to the power line by employing brachiation. The OTG produced two trajectories; one of which was reverse time symmetrical and; another which minimised the perpendicular distance between the end gripper and the power line. Linear interpolation between the two trajectories ensured a smooth bump-less trajectory for the BPLIR to follow

Fuzzy robust nonlinear control approach for electro-hydraulic flight motion simulator

AbstractA fuzzy robust nonlinear controller for hydraulic rotary actuators in flight motion simulators is proposed. Compared with other three-order models of hydraulic rotary actuators, the proposed controller based on first-order nonlinear model is more easily applied in practice, whose control law is relatively simple. It not only does not need high-order derivative of desired command, but also does not require the feedback signals of velocity, acceleration and jerk of hydraulic rotary actuators. Another advantage is that it does not rely on any information of friction, inertia force and external disturbing force/torque, which are always difficult to resolve in flight motion simulators. Due to the special composite vane seals of rectangular cross-section and goalpost shape used in hydraulic rotary actuators, the leakage model is more complicated than that of traditional linear hydraulic cylinders. Adaptive multi-input single-output (MISO) fuzzy compensators are introduced to estimate nonlinear uncertain functions about leakage and bulk modulus. Meanwhile, the decomposition of the uncertainties is used to reduce the total number of fuzzy rules. Different from other adaptive fuzzy compensators, a discontinuous projection mapping is employed to guarantee the estimation process to be bounded. Furthermore, with a sufficient number of fuzzy rules, the controller theoretically can guarantee asymptotic tracking performance in the presence of the above uncertainties, which is very important for high-accuracy tracking control of flight motion simulators. Comparative experimental results demonstrate the effectiveness of the proposed algorithm, which can guarantee transient performance and better final accurate tracking in the presence of uncertain nonlinearities and parametric uncertainties