Stéphane Caro

Multiobjective Design Optimization of 3–PRR Planar Parallel Manipulators

This chapter addresses the dimensional synthesis of parallel kinematics machines. A multiobjective optimization problem is proposed in order to determine optimum structural and geometric parameters of parallel manipulators. The proposed approach is applied to the optimum design of a three-degree-of-freedom planar parallel manipulator in order to minimize the mass of the mechanism in motion and to maximize its regular shaped workspace.

Finding the maximal pose error in robotic mechanical systems using constraint programming

The position and rotational errors --also called pose errors-- of the end-effector of a robotic mechanical system are partly due to its joints clearances, which are the play between their pairing elements. In this paper, we model the prediction of those errors by formulating two continuous constrained optimization problems that turn out to be NP-hard. We show that techniques based on numerical constraint programming can handle globally and rigorously those hard optimization problems. In particular, we present preliminary experiments where our global optimizer is very competitive compared to the best-performing methods presented in the literature, while providing more robust results.

Using Singularities of Parallel Manipulators to Enhance the Rigid-Body Replacement Design Method of Compliant Mechanisms

The rigid-body replacement method is often used when designing a compliant mechanism. The stiffness of the compliant mechanism, one of its main properties, is then highly dependent on the initial choice of a rigid-body architecture. In this paper, we propose to enhance the efficiency of the synthesis method by focusing on the architecture selection. This selection is done by considering the required mobilities and parallel manipulators in singularity to achieve them. Kinematic singularities of parallel structures are indeed advantageously used to propose compliant mechanisms with interesting stiffness properties. The approach is first illustrated by an example, the design of a one degree of freedom compliant architecture. Then, the method is used to design a medical device where a compliant mechanism with three degrees of freedom is needed. The interest of the approach is outlined after application of the method.

Stiffness Modelling of Parallelogram-Based Parallel Manipulators

The paper presents a methodology to enhance the stiffness analysis of parallel manipulators with parallelogram-based linkage. It directly takes into account the influence of the external loading and allows computing both the non-linear “load-deflection” relation and relevant rankdeficient stiffness matrix. An equivalent bar-type pseudo-rigid model is also proposed to describe the parallelogram stiffness by means of five mutually coupled virtual springs. The contributions of this paper are highlighted with a parallelogram-type linkage used in a manipulator from the Orthoglide family.

Practical Identifiability of the Manipulator Link Stiffness Parameters

The paper addresses a problem of the manipulator stiffness modeling, which is extremely important for the precise manufacturing of contemporary aeronautic materials where the machining force causes significant compliance errors in the robot end-effector position. The main contributions are in the area of the elastostatic parameters identification. Particular attention is paid to the practical identifiability of the model parameters, which completely differs from the theoretical one that relies on the rank of the observation matrix only, without taking into account essential differences in the model parameter magnitudes and the measurement noise impact. This problem is relatively new in robotics and essentially differs from that arising in geometrical calibration. To solve the problem, several physical and statistical model reduction methods are proposed. They are based on the stiffness matrix sparseness taking into account the physical properties of the manipulator elements and also on the heuristic selection of the practically non-identifiable parameters that employs numerical analyses of the parameter estimates. The advantages of the developed approach are illustrated by an application example that deals with the stiffness modeling of an industrial robot used in aerospace industry.

A Transmission Quality Index for a Class of Four-Limb Parallel Schönflies Motion Generators

This paper presents a uniform evaluation method for both transmission quality and singularity analysis for a class of parallel Schonflies-motion generators with four RRΠRR limbs. It turns out that the determinant of the forward Jacobian matrices for this class of parallel robots can be expressed as the scalar product of two vectors, the first vector being the cross product of the four unit vectors along the parallelograms, and the second one being related to the rotation of the mobile platform. The pressure angles, derived from the determinants of forward and inverse Jacobians, respectively, are used for the evaluation of the transmission quality and the detection of robot singularities. Five robots are compared based on the proposed indices as an illustrative example.

Dimensionally Homogeneous Jacobian and Condition Number

This paper deals with the formulation of the dimensionally homogeneous extended Jacobian matrix, which is an important issue for the performance analysis of f degrees-of-freedom (f ≤6) parallel manipulators having coupled rotational and translational motions. By using the f independent coordinates to define the permitted motions and (6-f) independent coordinates to define the restricted motions of the moving platform, the 6×6 dimensionally homogeneous extended Jacobian matrix is derived for non-redundant parallel manipulators. The conditioning number of the parallel manipulators is computed to evaluate the homogeneous extended Jacobian matrix, the homogeneous actuation wrench matrix, and the homogeneous constraint wrench matrix to evaluate the performance of the parallel manipulators. By using these indices, the closeness of a pose to different singularities can be detected. An illustrative example with the 3-RPS parallel manipulator is provided to highlight the effectiveness of the approach and the proposed indices.

Transmission Quality Evaluation for a Class of Four-limb Parallel Schönflies-motion Generators with Articulated Platforms

This paper investigated the motion/force transmission quality for a class of parallel Schonflies-motion generators built with four identical RRΠ RR-type limbs. It turns out that the determinant of the forward Jacobian matrices for this class of parallel robots can be expressed as the scalar product of two vectors, the first vector being the cross product of the four unit vectors along the parallelograms, the second one being related to the rotation of the mobile platform. The pressure angles, derived from the determinants of forward and inverse Jacobians, respectively, are used for the evaluation of the transmission quality of the robots. Four robots are compared based on the proposed method as illustrative examples.

Control of a Lower Mobility Dual Arm System.

This paper studies the kinematic modeling and control of two cooperative manipulators. The system is composed of the two arms of the humanoid Nao robot of Aldebaran. The serial structure of each arm has five degrees of freedom, in the closed chain formulation when transporting a common object, it has 4-DOF. The kinematic and dynamics representing the closed chain system is studied. A new control scheme demonstrates how the cooperative task space can be combined with a minimum representation of the task to control the 4 DOF of object. Furthermore by modeling the object grasp as a passive joint, we show that all 6-DOF of the object can be controlled.

Sensitivity and Dexterity Comparison of 3-RRR planar parallel manipulators

This paper deals with the sensitivity and dexterity comparison of 3-RRR planar parallel manipulators. First, the sensitivity coefficients of the pose of the moving platform of the manipulator to variations in its geometric parameters and actuated variables are derived and expressed algebraically. Moreover, two global sensitivity indices are determined, one related to the orientation of the moving platform of the manipulator and another one related to its position. The dexterity of the manipulator is also studied by means of the conditioning number of its normalized kinematic Jacobian matrix. Finally, the sensitivity of a 3-RRR PPM is analyzed in detail to compare the sensitivity of its best working mode to its dexterity.