Samuel Bouchard

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.

Computationally Efficient Predictive Robot Control

Conventional linear controllers (PID) are not really suitable for the control of robot manipulators due to the highly nonlinear behavior of the latter. Over the last decades, several control methods have been proposed to circumvent this limitation. This paper presents an approach to the control of manipulators using a computationally-efficient-model-based predictive control scheme. First, a general predictive control law is derived for position tracking and velocity control, taking into account the dynamic model of the robot, the prediction and control horizons, and also the constraints. However, the main contribution of this paper is the derivation of an analytical expression for the optimal control to be applied that does not involve a numerical procedure, as opposed to most predictive control schemes. In the last part of the paper, the effectiveness of the approach for the control of a nonlinear plant is illustrated using a direct-drive pendulum, and then, the approach is validated and compared to a PID controller using an experimental implementation on a 6-DOF cable-driven parallel manipulator.

Cyclic traction machine for long-term culture of fibroblast-populated collagen gels.

AbstractOur research group has been investigating the effect of cyclic deformations on the evolution of fibroblast populated collagen gels (FPCG). Since existing traction machines are not designed for such an application, we had to design a cyclic traction machine adapted to tissue culture inside an incubator over an extended period of time. Biocompatible materials were used for fabrication to allow for easy sterilization and to prevent any adverse reaction from the tissue. The traction machine is based on a computer-controlled stepping motor system for easy adjustment of the deformation amplitude and frequency. The maximum stretching speed achieved is around 1mm/s. The traction machine can measure FPCG mechanical properties and perform rupture tests to determine its ultimate strength. Several FPCGs have been successfully cultured with the machine for up to four weeks without any adverse reaction.

WORKSPACE OPTIMIZATION OF A VERY LARGE CABLE-DRIVEN PARALLEL MECHANISM FOR A RADIOTELESCOPE APPLICATION

The 6-DOF cable-driven mechanism under study in this paper is a feed positioning device for the Large Adaptive Reflector (LAR). The LAR is a concept of a very large orientable radio antenna. The study aims at optimizing the geometry of the cable mechanism to maximize the portion of the desired workspace in which the mechanism can remain in static equilibrium under the predicted external forces and torques. A general test to rapidly compute if the set of external forces and torques can be balanced is developed. This test is applicable to mechanisms with an arbitrary number(minimum six) of cables. Architectures with six to nine cables are optimized and compared. The conclusion of this study is that the prescribed task is unlikely to be achievable by this type of mechanism. Some design guidelines to improve the performance of a large cable-driven mechanism kept under tension by an aerostat are also provided.

On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches

This paper presents a new geometry-based method to determine if a cable-driven robot operating in a d-degree-of-freedom workspace (2 ≤ d ≤ 6) with n ≥ d cables can generate a given set of wrenches in a given pose, considering acceptable minimum and maximum tensions in the cables. To this end, the fundamental nature of the Available Wrench Set is studied. The latter concept, defined here, is closely related to similar sets introduced in [23, 4]. It is shown that the Available Wrench Set can be represented mathematically by a zonotope, a special class of convex polytopes. Using the properties of zonotopes, two methods to construct the Available Wrench Set are discussed. From the representation of the Available Wrench Set, computationally-efficient and non-iterative tests are presented to verify if this set includes the Task Wrench Set, the set of wrenches needed for a given task.Copyright

Kinematic Sensitivity of a Very Large Cable-Driven Parallel Mechanism

The LAR is a concept of a large orientable radiotelescope composed namely of a cable-driven parallel mechanism used to position and orient a feed plate. This document presents a first analysis of this mechanism’s orientation capability. The rotational kinematic sensitivity is defined here as the possible change in orientation occuring under a change in the actuation. After the application is described, common tools related to such problems are reviewed to explain why they are not totally suitable in this context. The velocity equation of the mechanism is then partitioned to obtain a quantification of the orientation kinematic sensitivity that is physically relevant. The study of a potential architecture’s rotational kinematic sensitivity is presented. Finally, the numerical and experimental validation of the approach are discussed. INTRODUCTION: THE LAR PROJECT The Large Adaptive Reflector (LAR), shown in figure 1, is a large orientable radio antenna concept being developed as a possible sub-element of a next generation radiotelescope called the Square Kilometer Array (SKA). The LAR appellation is due to the nature of its primary reflector, a section of a low curvature parabola made of several actuated triangular panels. The actuation enables the orientation of the reflecting surface towards the desired part of the sky. Legg first suggested such an approach in [12]. Its goal is to lower the cost per collecting unit area and to circumvent the structural limit of the current construction method for large orientable dishes. This is achieved by keeping the reflector close to the ground. The challenge of building such an antenna compared to building conventional ones is that the receiver feed is not rigidly attached to the reflector and so it must be positioned and oriented 1 Figure 1 Artist representation of the LAR. independently at a precision that depends on the wavelength observed, the technology used for the feed, and the optical arrangement. Also, because the reflector has a low curvature, its focal length is large. For the present LAR concept, this distance at which the feed must be placed from the centre of the reflector is 500 m. Dewdney and Veidt presented in [4] a first refinement to Legg’s initial suggestion. They concluded that a promising way to position the feed plate is to use a cable-driven parallel mechanism kept under tension by an aerostat filled with helium. This possibility was studied in more detail in [3] where the authors suggested the use of another level of actuation (the confluence point mechanism, CPM) at the focal apparatus to obtain the precision needed. The complete feed positioning system they envisioned is shown schematically in figure 2. It consists of two parallel mechanisms mounted in series. The large cable mechanism links the ground to the confluence point (CP) structure and performs coarse positioning and orientation Copyright

A Cable-driven Parallel Mechanism for Capturing Object Appearance from Multiple Viewpoints

This paper presents the full proof of concept of a system for capturing the light field of an object. It is based on a single high resolution camera that is moved all around the object on a cable-driven end-effector. The main advantages of this system are its scalability and low interference with scene lighting. The camera is accurately positioned along hemispheric trajectories by observing target features. From the set of gathered images, the visual hull is extracted and can be used as an approximate geometry for mapping a surface light field. The paper describes the acquisition system as well as the modeling process. The ability of the system to produce models is validated with four different objects whose sizes range from 20 cm to 3 m.

Motion Control of a Robot Manipulator in Free Space Based on Model Predictive Control

The majority of existing industrial manipulators are controlled using PD controllers. This type of basically linear control does not represent an optimal solution for the motion control of robots in free space because robots exhibit highly nonlinear kinematics and dynamics. In fact, in order to accommodate configurations in which gravity and inertia terms reach their minimum amplitude, the gain associated with the derivative feedback (D) must be set to a relatively large value, thereby leading to a generally over-damped behaviour that limits the performance. Nevertheless, in most current robotic applications, PD controllers are functional and sufficient due to the high reduction ratio of the transmissions used. However, this assumption is no longer valid for manipulators with low transmission ratios such as human-friendly manipulators or those intended to perform high accelerations like parallel robots. Over the last few decades, a new control approach based on the so-called Model Predictive Control (MPC) algorithm was proposed. Arising from the work of Kalman (Kalman, 1960) in the 1960’s, predictive control can be said to provide the possibility of controlling a system using a proactive rather than reactive scheme. Since this control method is mainly based on the recursive computing of the dynamic model of the process over a certain time horizon, it naturally made its first successful breakthrough in slow linear processes. Common current applications of this approach are typically found in the petroleum and chemical industries. Several attempts were made to adapt this computationally intensive method to the control of robot manipulators. A little more than a decade ago, it was proposed to apply predictive control to nonlinear robotic systems (Berlin & Frank, 1991), (Compas et al., 1994). However, in the latter references, only a restricted form of predictive control was presented and the implementation issues — including the computational burden — were not addressed. Later, predictive control was applied to a broader variety of robotic systems such as a 2-DOF (degree-of-freedom) serial manipulator (Zhang & Wang, 2005), robots with flexible joints (Von Wissel et al., 1994), or electrical motor drives (Kennel et al., 1987). More recently, (Hedjar et al., 2005), (Hedjar & Boucher, 2005) presented simplified approaches using a limited Taylor expansion. Due to their relatively low computation time, the latter approaches open the avenue to real-time implementations. Finally, (Poignet & Gautier, 2000), (Vivas et al., 2003), (Lydoire & Poignet, 2005), experimentally demonstrated