Reduced-Order Observer Design for Robot Manipulators

This paper investigates the design of reduced-order observers for robot manipulators. Observer stability conditions are obtained based on a Lyapunov analysis. The proposed observer is enhanced with a hybrid scheme that may adjust the gains to cope with possible unbounded velocities of the robot joints. Thanks to such hybrid strategy, the observer works accurately both for robots driven by open-loop controllers and by output feedback controllers. Numerical simulations illustrate the efficacy of the reduced-order observer in several scenarios, including a comparison with the performance of a classical full-order observer

Practical Model-based and Robust Control of Parallel Manipulators Using Passivity and Sliding Mode Theory

This chapter provides a practical strategy to realize accurate and robust control for 6 DOFs (degrees of freedom) parallel robots. The presented approach consists in two parts. The first basic part is based on the the compensation of the desired dynamics in combination with controller/observer for the single actuators. The passivity formalism offers an excellent framework to design and to tune the closed-loop dynamics, such that the desired behavior is obtained. The basic algorithm is proved to be locally robust towards uncertainties. The second part of the control strategy consists in a sliding mode controller. To keep the practical and computational efficient implementation, the proposed switching control considers explicitly only the friction model. Here we opt for the so called model-decomposition paradigm and we use additional integral action to improve robustness. The proposed approach is substantiated with experimental results demonstrating the effectiveness and success of the strategy that keeps control setup simple and intuitive. Keywords parallel manipulators, robust control, passivity formalism, sliding mode control, desired dynamics compensation, velocity observe

Robust state estimation for the control of flexible robotic manipulators

In this thesis, a novel robust estimation strategy for observing the system state variables of robotic manipulators with distributed flexibility is established. Motivation for the derived approach stems from the observation that lightweight, high speed, and large workspace robotic manipulators often suffer performance degradation because of inherent structural compliance. This flexibility often results in persistent residual vibration, which must be damped before useful work can resume. Inherent flexibility in robotic manipulators, then, increases cycle times and shortens the operational lives of the robots. Traditional compensation techniques, those which are commonly used for the control of rigid manipulators, can only approach a fraction of the open-loop system bandwidth without inducing significant excitation of the resonant dynamics. To improve the performance of these systems, the structural flexibility cannot simply be ignored, as it is when the links are significantly stiff and approximate rigid bodies. One thus needs a model to design a suitable compensator for the vibration, but any model developed to correct this problem will contain parametric error. And in the case of very lightly damped systems, like flexible robotic manipulators, this error can lead to instability of the control system for even small errors in system parameters. This work presents a systematic solution for the problem of robust state estimation for flexible manipulators in the presence of parametric modeling error. The solution includes: 1) a modeling strategy, 2) sensor selection and placement, and 3) a novel, multiple model estimator. Modeling of the FLASHMan flexible gantry manipulator is accomplished using a developed hybrid transfer matrix / assumed modes method (TMM/AMM) approach to determine an accurate low-order state space representation of the system dynamics. This model is utilized in a genetic algorithm optimization in determining the placement of MEMs accelerometers for robust estimation and observability of the system’s flexible state variables. The initial estimation method applied to the task of determining robust state estimates under conditions of parametric modeling error was of a sliding mode observer type. Evaluation of the method through analysis, simulations and experiments showed that the state estimates produced were inadequate. This led to the development of a novel, multiple model adaptive estimator. This estimator utilizes a bank of similarly designed sub-estimators and a selection algorithm to choose the true value from a given set of possible system parameter values as well as the correct state vector estimate. Simulation and experimental results are presented which demonstrate the applicability and effectiveness of the derived method for the task of state variable estimation for flexible robotic manipulators.Ph.D

Output Feedback Bilateral Teleoperation with Force Estimation in the Presence of Time Delays

This thesis presents a novel bilateral teleoperation algorithm for n degree of freedom nonlinear manipulators connected through time delays. Teleoperation has many practical uses, as there are many benefits that come from being able to operate machines from a distance. For instance, the ability to send a remote controlled robotic vehicle into a hazardous environment can be a great asset in many industrial applications. As well, the field of remote medicine can benefit from these technologies. A highly skilled surgeon could perform surgery on a patient who is located in another city, or even country. Earth to space operations and deep sea exploration are other areas where teleoperation is quite useful. Central to the approach presented in this work is the use of second order sliding mode unknown input observers for estimating the external forces acting on the manipulators. The use of these observers removes the need for both velocity and force sensors, leading to a lower cost hardware setup that provides all of the advantages of a position-force teleoperation algorithm. Stability results for this new algorithm are presented for several cases. Stability of each of the master and slave sides of the teleoperation system is demonstrated, showing that the master and slave are both stabilized by their respective controllers when the unknown input observers are used for state and force estimation. Additionally, closed loop stability results for the teleoperation system connected to a variety of slave side environments are presented. Delay-independent stability results for a linear spring-damper environment as well as a general finite-gain stable nonlinear environment are given. Delay-dependent stability results for the case where the slave environment is a liner spring-damper and the delays are commensurate are also presented. As well, stability results for the closed loop under the assumption that the human operator is modeled as a finite-gain stable nonlinear environment are given. Following the theoretical presentation, numerical simulations illustrating the algorithm are presented, and experimental results verifying the practical application of the approach are given

An energy based formalism for state estimation and motion control

This work presents an energy based state estimation formalism for a class of dynamical systems with inaccessible/unknown outputs and systems at which sensor utilization is costly, impractical or measurements can not be taken. The physical interactions among most of the dynamical subsystems represented mathematically in terms of Dirac structures allow power exchange through the power ports of these subsystems. Power exchange is conceptually considered as information exchange among the dynamical subsystems and further utilized to develop a natural feedback-like information from a class of dynamical systems with inaccessible/unknown outputs. The feedback-like information is utilized in realizing state observers for this class of dynamical systems. Necessary and sufficient conditions for observability are studied. In addition, estimation error asymptotic convergence stability of the proposed energy based state variable observer is proved for systems with linear and nonlinear dynamics. Robustness of the asymptotic convergence stability is analyzed over a range of parameter deviations, model uncertainties and unknown initial conditions. The proposed energy based state estimation formalism allows realization of the motion and force control from measurements taken from a single subsystem within the entire dynamical system. This in turn allows measurements to be taken from this single subsystem, whereas the rest of the dynamical system is kept free from measurements. Experiments are conducted on dynamical systems with single input and multiple inaccessible outputs in order to verify the validity of the proposed energy based state estimation and control formalism

Bond graph model based control of robotic manipulators

The performance of robotic manipulators is critical to their widespread use in industry. As manipulators become faster, their potential productivity can rise thus improving the return on the investment required to purchase them. Improving accuracy, on the other hand, increases the range of tasks for which the manipulator is suitable. The speed and accuracy of a manipulator is partly determined by the capability of the algorithm used to control it. Whilst being a highly non-linear multiple input, multiple output device, however, most industrial controllers are derived on the basis that the robot is a series of independent, linear actuator+ link subsystems. The resulting independent joint controller is simple to design and implement but is limited in its performance as link interactions and the non-linear effects of centrifugal and Coriolis forces degrade the accuracy at high manipulator velocities. Improvements in the control of manipulators may be made by incorporating a mathematical model of the manipulator in the control algorithm. Control schemes such as `computed torque' incorporate an inverse model of the manipulator to calculate the input torques required to force the end-effector to follow a desired trajectory. The equations of motion required to implement these controllers are large and complex even for relatively simple manipulators. This thesis explores how bond graph representations of robotic manipulators may be used to automate the implementation of model based controllers. To provide a practical basis for this research the bond graph derived controllers are tested on an experimental rigid, planar, direct drive two-link manipulator. It is shown how the bondgraph for this manipulator, including d.c. motor actuators, can be constructed and used to derive the equations of motion of the manipulator automatically. The bond graph model is then validated by comparing simulations obtained using these equations of motion with experimental data