Vicente Mata

Serial-robot dynamics algorithms for moderately large numbers of joints

Abstract A method for solving the complete dynamic problem in robots with rigid links and ideal joints using the Gibbs–Appell equations as starting point is presented. The inverse dynamic problem is solved through a algorithm O(n), where tensor notation is used. The terms of the generalized inertia matrix are calculated by means of the Hessian of the Gibbs function with respect to generalized accelerations, and a recursive algorithm of order O(n2) is developed. Proposed algorithms are computationally efficient for serial-robots with moderately large numbers of joints. The numerical stability of the proposed algorithms is analyzed and compared with those of other methods by the use of numerical examples.

A comparison between direct and indirect dynamic parameter identification methods in industrial robots

The estimation of dynamic parameters in mechanical systems constitutes an issue of crucial importance both for inverse dynamics based control strategies and dynamic simulation applications where high accuracy is required. The identification procedures can be classified in two main groups: indirect and direct procedures. The first ones act sequentially in several steps in each of them parameters of different nature (basically friction and inertial parameters) are identified by means of specifically designed experiments, while the direct procedures allow the identification of all parameters defining de dynamic model in a single stage. In this paper, the implementation and comparison of an indirect and a direct identification procedures on an industrial robot provided with an open control architecture is addressed.

Dynamic parameter identification in industrial robots considering physical feasibility

The issue of identification of dynamic parameters in open-chain industrial manipulators is addressed with emphasis on the physical feasibility of the identified set of parameters. The dynamic model on which the identification procedure is based considers rigid-link robots including a complete actuator dynamics modeling and is obtained starting from the Gibbs–Appell equations. Friction at the joints is also considered. The dynamic equations of the model are written linearly with respect to the dynamic parameters to be identified. The matrix form linear system is solved through a quadratic optimization procedure with non-linear constraints in order to ensure the physical feasibility of the identified parameters. The procedure is tested using a PUMA 560 industrial robot. A comparison between control actions and torques obtained from the Inverse Dynamic Problem considering identified parameters is performed in order to establish the validity of the proposed procedure. The set of physically feasible dynamic parameters is used in an integration of the equations of motion of the robot and the results of the simulation are compared with the robot actual movement.

Model-Based Control of a 3-DOF Parallel Robot Based on Identified Relevant Parameters

This paper presents in detail how to model, identify, and control a 3-DOF prismatics-revolute-spherical parallel manipulator in terms of relevant parameters. A reduced model based on a set of relevant parameters is obtained following a novel approach that considers a simplified dynamic model with a physically feasible set of parameters. The proposed control system is compared with the response of a model-based control that considers the complete identification of the rigid-body dynamic parameters, friction at joints, and the inertia of the actuators. The control systems are implemented on a virtual and an actual prototype. The results show that the control scheme based on the reduced model improves the trajectory tracking precision when comparing with the control scheme based on the complete set of dynamic parameters. Moreover, the reduced model shows a significant reduction in the computational burden, allowing real-time control.

Kinematic description of soft tissue artifacts: quantifying rigid versus deformation components and their relation with bone motion

This paper proposes a kinematic approach for describing soft tissue artifacts (STA) in human movement analysis. Artifacts are represented as the field of relative displacements of markers with respect to the bone. This field has two components: deformation component (symmetric field) and rigid motion (skew-symmetric field). Only the skew-symmetric component propagates as an error to the joint variables, whereas the deformation component is filtered in the kinematic analysis process. Finally, a simple technique is proposed for analyzing the sources of variability to determine which part of the artifact may be modeled as an effect of the motion, and which part is due to other sources. This method has been applied to the analysis of the shank movement induced by vertical vibration in 10 subjects. The results show that the cluster deformation is very small with respect to the rigid component. Moreover, both components show a strong relationship with the movement of the tibia. These results suggest that artifacts can be modeled effectively as a systematic relative rigid movement of the marker cluster with respect to the underlying bone. This may be useful for assessing the potential effectiveness of the usual strategies for compensating for STA.

Mechatronic Development and Dynamic Control of a 3-DOF Parallel Manipulator

The aim of this article is to develop, from the mechatronic point of view, a low-cost parallel manipulator (PM) with 3-degrees of freedom (DOF). The robot has to be able to generate and control one translational motion (heave) and two rotary motions (rolling and pitching). Applications for this kind of parallel manipulator can be found at least in driving-motion simulation and in the biomechanical field. An open control architecture has been developed for this manipulator, which allows implementing and testing different dynamic control schemes for a PM with 3-DOF. Thus, the robot developed can be used as a test bench where control schemes can be tested. In this article, several control schemes are proposed and the tracking control responses are compared. The schemes considered are based on passivity-based control and inverse dynamic control. The control algorithm considers point-to-point control or tracking control. When the controller considers the system dynamics, an identified model has been used. The control schemes have been tested on a virtual robot and on the actual prototype.

A formulation for path planning of manipulators in complex environments by using adjacent configurations

The problem of robot path planning among obstacles has been approached by formulating robot configurations by means of a suitable fully Cartesian coordinate description. Thus, an analytical express...

Effect of marker cluster design on the accuracy of human movement analysis using stereophotogrammetry

This paper presents a new, simple model to evaluate the instrumental random errors in kinematic analysis of human movements using stereophotogrammetry. By means of equations analogous to that relate linear or angular momentum with linear or angular velocities, a direct measurement of instantaneous motion can be made without previous finite displacement analysis. Single explicit expressions can be obtained to evaluate the influence of instrumental random errors in the accuracy of the kinematic variables. From these expressions, some conclusions about the effect of marker cluster design on the experimental errors are obtained. An experiment has been carried out in order to validate the proposed technique and to assess the experimental errors in linear and angular velocity measurement and its influence in instantaneous helical axis determination.

Identifiability of the Dynamic Parameters of a Class of Parallel Robots in the Presence of Measurement Noise and Modeling Discrepancy

Abstract Advanced model-based control schemes and the solution of the direct dynamic problem require accurate knowledge of the dynamic parameters of robotic systems, mainly the inertial properties of the links and the friction parameters at the kinematic joints. A well-known and a very useful tool for their determination is through a dynamic identification process. Normally, in this process, only a subset of the dynamic parameters of a robot, known as “base parameters,” can be identified. When parameter identification is performed experimentally, not all the aspects of the robot can be modeled in detail. Moreover, measurement variables are affected by noise. These sources of error lead to the fact that not all the base parameters can be properly identified. Therefore, in this paper, the identifiability of the dynamic parameters of a class of parallel robot, in the presence of noise in measurement and discrepancy in modeling, is addressed. The analysis is carried out by means of a simulated robot and over an actual parallel 3-RPS robot.

Dynamic simulation of a parallel robot: Coulomb friction and stick–slip in robot joints

Dynamic simulation in robotic systems can be considered as a useful tool not only for the design of both mechanical and control systems, but also for planning the tasks of robotic systems. Usually, the dynamic model suffers from discontinuities in some parts of it, such as the use of Coulomb friction model and the contact problem. These discontinuities could lead to stiff differential equations in the simulation process. In this paper, we present an algorithm that solves the discontinuity problem of the Coulomb friction model without applying any normalization. It consists of the application of an external switch that divides the integration interval into subintervals, the calculation of the friction force in the stick phase, and further improvements that enhance its stability. This algorithm can be implemented directly in the available commercial integration routines with event-detecting capability. Results are shown by a simulation process of a simple 1-DoF oscillator and a 3-DoF parallel robot prototype considering Coulomb friction in its joints. Both simulations show that the stiffness problem has been solved. This algorithm is presented in the form of a flowchart that can be extended to solve other types of discontinuity.