Eusebio Hernandez

Orientation of radio-telescope secondary mirror via adaptive sliding mode control

In this work a parallel manipulator (Stewart platform) is used to align and maintain the position of the secondary mirror of a radio-telescope. The six degrees of freedom platform gives the significant advantage of reaching the maximum performance for the positioning tasks. The near-singularity condition of the platform is analyzed and is handled by implementation of a new control law based on sliding mode with inner regularization procedure. Herein, the finite-time convergence of closed-loop system derived from designed control in the presence of external as well as internal disturbances/uncertainties is proved. The effectiveness of the proposed controller is verified via numerical simulation. We show that Sliding Mode Control with a gain matrix adaptation based on the Equivalent Control method can significantly reduce the undesirable chattering effect an therefore avoid the possible damages.

Structure-control design of a mechatronic system with parallelogram mechanism using an estimation of distribution algorithm

ABSTRACT In this paper, a structure-control design methodology for simultaneously optimizing both mechanical structure and control of a parallelogram linkage robot is proposed. It takes into count the dynamical model and the mechanical parameters for the optimization process along with the controller. Thus, proportional-integral-derivative (PID) control and geometric variables are optimized in a simultaneously way. Through the concurrent procedure an optimal combination of the robot structure and controller gains is obtained. The global optimization problem is tackled by using an estimation of distribution algorithm (EDA) based on the Boltzmann distribution. The EDA seeks for the global optimum by estimating and sampling a probability distribution. The proposed methodology is verified through simulation experiments and applied to the design process of a parallelogram linkage system. The results obtained in experiments show the effectiveness of the proposal. This approach is generic and could be applied to other mechanisms in similar way when for concurrent process both kinematic and dynamic models are available along with the controller. In particular, the results are promising when the optimization parameters are uncorrelated, namely control and mechanical parameters.

A comparison of simulations and experimental tests on operation performance of CaPaMan2 bis

In this paper, operation performance of CaPaMan2 bis (Cassino Parallel Manipulator2 bis) has been investigated through numerical simulations and lab experimental tests. A 3D (three dimension) virtual model has been built in MSC.ADAMS environment to simulate the operation behaviour for different prescribed motions. Milli-CaTraSys (Milli-Cassino Tracking System) has been implemented to measure position and orientation of the platform of the prototype CaPaMan2 bis during experimental tests. Several prescribed motions have been simulated and tested under different conditions in order to characterize the system behaviour. Finally, experiment results and simulation computations have been compared for the purpose of performance evaluation and design characterization of the manipulator structure and its prototype.

Design Optimization of a Cable-Driven Parallel Robot in Upper Arm Training-Rehabilitation Processes

This paper presents an optimized design of a cable driven parallel manipulator which is intended in rehabilitation or exercise of patients with shoulder problems like illness, traumatic events or for the elderly who need to exercise their limbs. Cable based parallel manipulators have characteristics that make them suitable for rehabilitation-exercise purposes like large workspace, re-configurable architecture, portability and low cost. From these purposes, upper-limb movements are analyzed and different prescribed workspaces are defined. After kinematic and wrench analysis, the Jacobian matrix of the cable driven manipulator is derived, which is used as a quantitative representation of dexterity along the workspace. An optimization model is presented to simultaneously fulfill the prescribed workspace and to improve dexterity by selecting proper length cables and other structural parameters. Numerical examples delineate effectiveness of an Estimation of Distribution Algorithm (EDA), where correlation among variables are inserted in the optimization process.

Adaptive sliding-mode controller based on the “Super-Twist” state observer for control of the Stewart platform

To provide a highly efficient control of nonlinear systems in the presence of nonmodeled dynamics and external perturbations, a new control law with feedback based on the sliding modes with an observer of the “Super-Twist” kind was proposed. For acceptable use of the continuous observer signal in the controller, presented were adaptive laws for adjustment of the control system parameters. Using the methods of Lyapunov function, system stability (convergence to a zone) was proved. This technique was proposed as an example of control and stabilization of the position of a parallel manipulator (Gough–Stewart platform). The presented mechanism with six degrees of freedom is used to control the secondary mirror of the “Large Millimeter Telescope Alfonso Serrano” situated in the state of Puebla, Mexico.

Concurrent Structure-Control Design of Parallel Robots Using an Estimation of Distribution Algorithm

In this paper, a structure-control design methodology for simultaneously optimizing both mechanical structure and control of parallel robots is proposed. It takes into count the dynamical model and the mechanical parameters for the optimization process. Thus, PID control and geometric variables are optimized in a simultaneously way. Through the concurrent procedure, an optimal combination of the robot structure and control gains is obtained. An estimation of distribution algorithm (EDA) is formulated and used as the search algorithm. The proposed methodology is verified through simulation experiments and applied to the design process of a parallelogram linkage system. The results obtained in experiments show the effectiveness of the proposed methodology. The presented approach is generic and can be applied to other mechanisms with similar structure.

On the Numerical Modelling and Error Compensation for General Gough-Stewart Platform

Parallel robots are specially designed to perform high-precision tasks. Nevertheless, manufacturing, assembling and control issues can reduce their capacity to perform adequately. Observing the acquired measurement data with high-precision devices - such as laser-based instruments - it is not surprising that the error data follows patterns or have a structure because, in many cases, the greatest error comes from a mechanical bias introduced by manufacturing issues. Even though we cannot determine with certainty where the error comes from, a pattern in the measured data suggests that it is feasible that it can be modelled and corrected - in a significant proportion - by purely software applications, without the need of disassembling or re-manufacturing any component. This work deals with the problem of finding a mathematical model which adequately fits the error data from the legs of a general Gough-Stewart platform. Hence, we obtain an expression which can be subtracted from the control parameters in order to compensate the inherent mechanical error in the legs. The purpose of this article is two-fold: 1) to present numerical results of the beneficial effects of the error compensation in the legs as well as in the end-effector, and 2) to introduce a numerical methodology to find a model for error compensation and to numerically simulate its effects. Numerical, graphical and statistical evidence of the error improvements, according this methodology, is provided.

Design and Control Strategy of a Low-Cost Parallel Robot for Precise Solar Tracking

This paper presents the design of a new 2 degrees of freedom parallel manipulator and its theoretical implementation as a precise solar tracker. The cinematic mathematical model of the mechanism is studied in detail and a robust control algorithm based on sliding mode control is introduced to perform the desired angular positions and velocities in the presence of disturbances/uncertainties. The numerical simulations are carried out to verify the behavior of the suggested controller.

Approach in the Integrated Structure-Control Optimization of a 3RRR Parallel Robot

In this paper, an optimization methodology for the structure and control optimization of a 3RRR planar parallel robot is presented. The proposal consists of three stages in cascade: firstly, we optimize the geometry for a maximum workspace. Secondly, the kinematics is used to optimize dexterity for a set of desired paths inside the workspace that is found in the first stage, and, finally, a set of dynamic control gains are optimized for trajectories given by the same paths. The methodology permits to reduce the computational cost for the geometry optimization stages, while optimizing the control gains using high precision numerical simulation using SimWise 4D commercial software, with a reduced number of evaluations of candidate solutions, and as consequence, a reduced computational time. The results demonstrate that the final structure-control optimized design accurately follows the desired trajectories.

Orientation of radio-telescope secondary mirror via parallel platform

In this work a parallel manipulator (Stewart platform) is used to align and maintain the position of the secondary mirror of a radio-telescope. The six degree of freedom platform gives the significant advantage to reach the maximum performance for the positioning task. This system uses six lineal actuators with changeable lengths to obtain the desired position. The filtered version of sliding mode algorithm is used to control and orient the system in presence of unmodelled dynamics and perturbations. It provides chattering effect reduction and improving of the performance of the system.