Philippe Cardou

Kinematic-Sensitivity Indices for Dimensionally Nonhomogeneous Jacobian Matrices

Numerous performance indices have been proposed to compare robot architectures based on their kinematic properties. However, none of these indices seems to draw a consensus among the robotics community. The most notorious indices, which are manipulability and dexterity, still entail some drawbacks, which are mainly due to the impossibility to define a single invariant metric for the special Euclidean group. The natural consequence is to use two distinct metrics, i.e., one for rotations and one for point displacements, as has already been proposed by other researchers. This is the approach used in this paper, where we define the maximum rotation sensitivity and the maximum point-displacement sensitivity. These two indices provide tight upper bounds to the end-effector rotation and point-displacement sensitivity under a unit-magnitude array of actuated-joint displacements. Therefore, their meaning is thought to be clear and definite to the designer of a robotic manipulator. Furthermore, methods for the computation of the proposed indices are devised, some of their properties are established and interpreted in the context of robotic manipulator design, and an example is provided.

Geometric Determination of the Interference-Free Constant-Orientation Workspace of Parallel Cable-Driven Mechanisms

The increasing use of parallel cable-driven mechanisms calls for a better understanding of their behavior and highly efficient algorithms to attenuate their drawbacks at the design stage. One of these drawbacks is the high probability of mechanical interferences between the moving parts of the mechanism. In this paper, the phenomenon is described under the assumption that a cable is a line segment in space. When a mechanical contact occurs between two cables or between a cable and an edge of the end effector, these entities necessarily lie in the same plane, and then the three-dimensional problem becomes two-dimensional. This fact is used to simplify the equations, and leads to exhaustive descriptions of the associated interference loci in the constant-orientation workspace of a cable-driven mechanism. These results provide a fast method to graphically represent all interference regions in the manipulator workspace, given its geometry and the orientation of its end effector.

The Kinematic Sensitivity of Robotic Manipulators to Joint Clearances

The paper deals with the kinematic sensitivity of robotic manipulators to joint clearances. First, an error prediction model applicable to both serial and parallel manipulators is developed. A clearance model associated with axisymmetrical joints, which are widely used in robotic manipulators, is also proposed. Then, two nonconvex quadratically constrained quadratic programs (QCQPs) are formulated in order to find the maximum reference-point position error and the maximum orientation error of the moving-platform for given joint clearances. Finally, the contributions of the paper are highlighted by means of two illustrative examples.Copyright

Measuring How Well a Structure Supports Varying External Wrenches

An index is introduced, the minimum degree of constraint satisfaction, which quantifies the robustness of the equilibrium of an object with a single scalar. This index is defined under the assumptions that the object is supported by forces of known lines of action and bounded amplitudes, and that the external perturbation forces and moments vary within a known set of possibilities. A method is proposed to compute the minimum degree of constraint satisfaction by resorting to the quick hull algorithm. The method is then applied to two examples chosen for their simplicity and diversity, as evidence of the broad spectrum of applications that can benefit from the index. The first example tackles the issue of fastening a workpiece, and the second, the workspace of a cable-driven parallel robot. From these numerical experiments, the minimum degree of constraint satisfaction proves useful in grasping, cable-driven parallel robots, Gough-Stewart platforms and other applications.

ARACHNIS: Analysis of Robots Actuated by Cables with Handy and Neat Interface Software

This paper presents ARACHNIS, a graphical user interface for the analysis and parametric design of Cable Driven Parallel Robots (CDPRs). ARACHNIS takes as inputs the design parameters of the robot, the task specifications, and returns a visualisation of the CDPR Wrench Feasible Workspace (WFW) and Interference-Free Constant Orientation Workspace (IFCOW). The WFW is traced from the capacity margin, a measure of the robustness of the equilibrium of the robot. Interferences between the moving parts of a CDPR are also determined by an existing technique for tracing the interference-free workspace of such robots. Finally, the WFW and the IFCOW of a planar cable-driven parallel robot and of a spatial cable-driven parallel robot are plotted in order to demonstrate the potential of ARACHNIS.

A Smart Safety Helmet using IMU and EEG sensors for worker fatigue detection

It is known that head gesture and brain activity can reflect some human behaviors related to a risk of accident when using machine-tools. The research presented in this paper aims at reducing the risk of injury and thus increase worker safety. Instead of using camera, this paper presents a Smart Safety Helmet (SSH) in order to track the head gestures and the brain activity of the worker to recognize anomalous behavior. Information extracted from SSH is used for computing risk of an accident (a safety level) for preventing and reducing injuries or accidents. The SSH system is an inexpensive, non-intrusive, non-invasive, and non-vision-based system, which consists of an Inertial Measurement Unit (IMU) and dry EEG electrodes. A haptic device, such as vibrotactile motor, is integrated to the helmet in order to alert the operator when computed risk level (fatigue, high stress or error) reaches a threshold. Once the risk level of accident breaks the threshold, a signal will be sent wirelessly to stop the relevant machine tool or process.

Angular Velocity Estimation From the Angular Acceleration Matrix

Computing the angular velocity ω from the angular acceleration matrix is a nonlinear problem that arises when one wants to estimate the three-dimensional angular velocity of a rigid-body from point-acceleration measurements. In this paper, two new methods are proposed, which compute estimates of the angular velocity from the symmetric part W S of the angular acceleration matrix. The first method uses a change of coordinate frame of W S prior to performing the square-root operations. The new coordinate frame is an optimal representation of W S with respect to the overall error amplification. In the second method, the eigenvector spanning the null space of W S is estimated. As w lies in this space, and because its magnitude is proportional to the absolute value of the trace of W S , it is a simple matter to obtain w. A simulation shows that, for this example, the proposed methods are more accurate than those existing methods that use only centripetal acceleration measurements. Moreover, their errors are comparable to other existing methods that combine tangential and centripetal acceleration measurements. In addition, errors of 2.15% in the accelerometer measurements result in errors of approximately 3% in the angular-velocity estimates. This shows that accelerometers are competitive with angular-rate sensors for motions of the type of the simulated example, provided that position and orientation errors of the accelerometers are accounted for.

A Nonlinear Program for Angular-Velocity Estimation From Centripetal-Acceleration Measurements

Measuring the trajectory of a rigid body in space is commonly done using an inertial measurement unit composed of one triaxial accelerometer and one triaxial gyroscope. When the rigid body undergoes high accelerations, it is often preferable to resort to an array of accelerometers rather than the traditional accelerometer-gyroscope combination, an approach that is now common in crashworthiness and other biomechanics applications. In this paper, we present an algorithm for the estimation of the rigid-body angular velocity from the centripetal components of the accelerations measured by the array of accelerometers. The proposed algorithm and the others available in the literature were benchmarked using the accelerometer array octahedral constellation of twelve accelerometers. In the reported testing conditions, the proposed method is slightly more robust than any other based on centripetal-acceleration measurements.

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.

Linear Estimation of the Rigid-Body Acceleration Field From Point-Acceleration Measurements

Among other applications, accelerometer arrays have been used extensively in crashworthiness to measure the acceleration field of the head of a dummy subjected to impact. As it turns out, most accelerometer arrays proposed in the literature were analyzed on a case-by-case basis, often not knowing what components of the rigid-body acceleration field the sensor allows to estimate. We introduce a general model of accelerometer behavior, which encompasses the features of all acclerometer arrays proposed in the literature, with the purpose of determining their scope and limitations. The model proposed leads to a classification of accelerometer arrays into three types: point-determined; tangentially determined; and radially determined. The conditions that define each type are established, then applied to the three types drawn from the literature. The model proposed lends itself to a symbolic manipulation, which can be readily automated, with the purpose of providing an evaluation tool for any acceleration array, which should be invaluable at the development stage, especially when a rich set of variants is proposed.