Fernando Reyes-Cortés

Experimental evaluation of parameter identification schemes on a direct-drive robot:

The dynamic and friction parameters of a robot are used in advanced control schemes, and their accuracy significantly affects their performance. These parameters can also be used for a realistic simulation. In principle, the numerical value of the parameters could be obtained via computer-aided design analysis but inevitable assembly and manufacturing errors exist. Direct measurement is not a realistic option because the complex nature of the system would involve an intense time-consuming effort. Alternatively, we can deduce the values of the parameters by observing the natural response of the system under appropriate experimental conditions, that is, by using identification schemes. This article presents the experimental evaluation of five identification schemes used to obtain the dynamic and friction parameters of a two-degree-of-freedom, direct-drive robot. We assume that the dynamic and friction parameters are totally unknown but, by design, the dynamic model is fully known. We consider the schemes based on the dynamic regression model, filtered-dynamic regression model, supplied-energy regression model, power regression model, and filtered-power regression model. The article presents a comparison between experimental and simulated robot responses, which enable us to verify the accuracy of each regression model.

Experimental Evaluation of Parameter Identification Schemes on an Anthropomorphic Direct Drive Robot

The inertial and friction parameters of a robot are used in the development and evaluation of model-based control schemes and their accuracy is related directly to the performance. These parameters can also be used for a realistic simulation, which may be useful before implementation of new control schemes. In principle, the numerical value of the parameters could be obtained via CAD analysis, but inevitably assembly and manufacturing errors exist. Direct measurement is not a realistic option because the complex nature of the system involves intense, time-consuming effort. Alternatively, we can deduce the values of the parameters by observing the natural response of the system under appropriate experimental conditions, i.e., by using identification schemes, which is an efficient way. This paper presents the experimental evaluation of five identification schemes used to obtain the inertial and friction parameters of a three-degrees-of-freedom direct-drive robot. We assume that the inertial and friction parameters are totally unknown but, by design, the dynamic model is fully known, as in many practical cases. We consider the schemes based on the dynamic regression model, the filtered-dynamic regression model, the supplied-energy regression model, the power regression model and the filtered-power regression model. This paper presents a comparison between experimental and simulated robot response, which enables us to verify the accuracy of each regression model.

Cartesian Control for Robot Manipulators

A robot is a reprogrammable multi-functional manipulator designed to move materials, parts, tools, or specialized devices through variable programmed motions, all this for a best performance in a variety of tasks. A useful robot is the one which is able to control its movements and the forces it applies to its environment. Typically, robot manipulators are studied in consideration of their displacements on joint space, in other words, robot’s displacements inside of its workspace usually are considered as joint displacements, for this reason the robot is analyzed in a joint space reference. These considerations generate an important and complex theory of control in which many physical characteristics appear, this kind of control is known as joint control. The joint control theory expresses the relations of position, velocity and acceleration of the robot in its native language, in other words, describes its movements using the torque and angles necessary to complete the task; in majority of cases this language is difficult to understand by the end user who interprets space movements in cartesian space easily. The singularities in the boundary workspace are those which occur when the manipulator is completely strechedout or folded back on itself such as the end-effector is near or at the boundary workspace. It’s necessary to understand that singularity is a mathematical problem that undefined the system, that is, indicates the absence of velocity control which specifies that the end-effector never get the desired position at some specific point in the workspace, this doesn’t mean the robot cannot reach the desired position structurally, whenever this position is defined inside the workspace. This problem was solved by S. Arimoto and M. Takegaki in 1981 when they proposed a new control scheme based on the Jacobian Transposed matrix; eliminating the possibility of singularities and giving origin to the cartesian control. The joint control is used for determining the main characteristics of the cartesian control based on the Jacobian Transposed matrix. It is necessary to keep in mind that to consider the robot’s workspace like a joint space, has some problems with interpretation because the user needs having a joint dimensional knowledge, thus, when the user wants to move the robot’s endeffector through a desired position he needs to understand the joint displacements the robot needs to do, to get the desired position. This interpretation problem is solved by using the cartesian space, that is, to interpret the robot’s movements by using cartesian coordinates on reference of cartesian space; the advantage is for the final user who has the cartesian dimensional knowledge for understanding the robot’s movements. Due this reason, learning the mathematical tools for analysis by the robot’s movements on cartesian space is necessary, this allows us to propose control structures, to use the dynamic model and to understand the 8

On Stiffness Regulators with Dissipative Injection for Robot Manipulators

The stiffness controller proposed by Salisbury is an interaction control strategy designed to achieve a desired form of static behavior as regards the interaction of a robot manipulator with the environment. The main idea behind this approach is the simulation of a multidimensional linear spring - or linear elastic material - using the difference between the actual position of the end-effector and a constant position (relaxed point), multiplied by a constant stiffness matrix. In this paper, this idea is generalized with the objective of proposing a controller structure that includes a family of stiffness models based on the idea of linear elastic materials. The new controller structure also includes a damping term in order to have control over energy dissipation, as well as a term added for the purpose of compensating the gravity forces of the links. The stability analysis of the proposed controller was performed in the Lyapunov sense. The new stiffness controller is presented as a case study and compared to other cases, such as the Salisbury controller (Cartesian PD) and the tanh-tanh controller. Experimental results using a three degrees-of-freedom direct-drive robot for the evaluation of controllers in a constrained motion task are presented.

New control structure in Cartesian space

The main objective of this paper is to propose a new controller scheme for robot manipulators on Cartesian space with formal stability proof. To verify the performance of the proposed controller we compared its behavior with the Cartesian PD controller. In this paper we described an experimental Cartesian robot for research and development of robot control algorithms. This system allows the development and easy test of Cartesian control strategies on three degrees of freedom. The functionality of this system is explained via real-time experimental results of a new position control algorithm with global asymptotic stability of the closed-loop system

A Family of Hyperbolic-Type Explicit Force Regulators with Active Velocity Damping for Robot Manipulators

This paper addresses the explicit force regulation problem for robot manipulators in interaction tasks. A new family of explicit force-control schemes is presented, which includes a term driven by a large class of saturated-type hyperbolic functions to handle the force error. Also, an active velocity damping term with the purpose of obtaining energy dissipation on the contact surface is incorporated plus compensation for gravity. In order to ensure asymptotic stability of the closed-loop system equilibrium point in Cartesian space, we propose a strict Lyapunov function. A force sensor placed at the end-effector of the robot manipulator is used in order to feed back the measure of the force error in the closed-loop, and an experimental comparison of the performance -norm between 5 explicit force control schemes, which are the classical proportional-derivative (PD), arctangent, and square-root controls and two members of the proposed control family, on a two-degree-of-freedom, direct-drive robot manipulator, is presented.

Unbounded regulators with variable gains for a direct-drive robot manipulator

This paper addresses the position-control problem with variable gains for robot manipulators. We present a new regulator based on a hyperbolic-sine structure with tuning rules for control gains. It is demonstrated that the equilibrium point of the closed-loop system is globally, asymptotically stable according to Lyapunov theory. By using a similar methodology, this concept can be extended to other unbounded controllers such as PD and PID. In order to show the usefulness of the proposed scheme and with the purpose of validating its asymptotical stability property, an experimental comparison involving constant gains controllers, for example: simple PD, PID and hyperbolic-tangent schemes vs variable-gains hyperbolic-sine and PD control schemes, was performed by using a three degree-of-freedom, direct-drive robot manipulator.

Cartesian Controller's Evaluation in Joint Space

This paper addresses the problem of position control for robot manipulators. A new family of controllers for robot manipulators on Cartesian coordinates with gravity compensation is presented. The simple PD-type Cartesian controller can be found among this family of controllers. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear robot dynamics and the new family is asymptotically stable in local sense in agreement with Lyapunovs direct method and La Salles invariance principle. To illustrate the performance of new controllers family, time-real experimental results on a two degrees of freedom direct-drive arm are also presented