Roger Boudreau

The Synthesis of Planar Parallel Manipulators with a Genetic Algorithm

This paper presents a genetic algorithm approach for the synthesis of planar three-degree-of-freedom parallel manipulators. A genetic algorithm is an optimization method inspired by natural evolution. As in nature, the fittest members of a population are given better chances of reproducing and transmitting part of their genetic heritage to the next generation. This leads to stronger and stronger generations which evolve towards the solution of the problem. For the applications studied here, the individuals in the population consist of the architectural parameters of the manipulators. The algorithm optimizes these parameters to obtain a workspace as close as possible to a prescribed working area. For each individual of the population, the geometric description of the workspace can be obtained. The algorithm then determines the intersection between the prescribed workspace and the actual workspace, and minimizes the area of the regions that do not intersect. The method is applied to two planar three-degree-of-freedom parallel manipulators, one with prismatic joints and one with revolute joints.

Solving the forward kinematics of parallel manipulators with a genetic algorithm

A floating point genetic algorithm is proposed to solve the forward kinematic problem for parallel manipulators. This method, adapted from studies in the biological sciences, allows the use of inverse kinematic solutions to solve forward kinematics as an optimization problem. The method is applied to two 3-degree-of-freedom planar parallel manipulators and to a 3-degree-of-freedom spherical manipulator. The method converges to a solution within a broader search domain compared to a Newton-Raphson scheme.

Real-coded genetic algorithm for Bragg grating parameter synthesis

We propose to use a genetic algorithm to determine the physical parameters of Bragg gratings from their reflection spectra for both design purposes and fiber sensor applications. A real-coded genetic algorithm is used for inversion purposes, along with an F-matrix formalism for synthesis of uniform, chirped, and apodized gratings. An example of bandpass filter design is also studied. The method is easily applicable and shows promising results.

A Family of Kinematically Redundant Planar Parallel Manipulators

Parallel manipulators feature relatively high payload and accuracy capabilities compared to their serial counterparts. However, they suffer from small workspace and low maneuverability. Kinematic redundancy for parallel manipulators can improve both of these characteristics. This paper presents a family of new kinematically redundant planar parallel manipulators with six actuated-joint degrees of freedom based on a 3-PRRR architecture obtained by adding an active prismatic joint at the base of each limb of the 3-RRR manipulator. First, the inverse displacement of the manipulators is explained, then their reachable and dexterous workspaces are obtained. Comparing the proposed redundant manipulators to the original 3-RRR nonredundant manipulator, both reachable and dexterous workspaces are substantially larger. Next, the Jacobian matrices of the manipulators are derived, and different types of singularities are analyzed and demonstrated. It is shown that the vast majority of singularities can be avoided by using kinematic redundancy.

La synthèse d'une plate-forme de Gough-Stewart pour un espace atteignable prescrit

Abstract This paper presents a genetic algorithm approach to determine the architectural parameters of a Stewart-Gough platform that has a workspace as close as possible to a prescribed workspace. The algorithm used determines the intersection between the actual workspace and the prescribed one. The genetic algorithm then optimizes 26 architectural parameters to minimize the area of the regions that do not intersect. The optimization can be performed for a fixed orientation of the platform, for an orientation that varies about a certain axis, or for different platform elevations.

On the computation of the direct kinematics of parallel manipulators using polynomial networks

Polynomial learning networks are proposed in this paper to solve the forward kinematic problem for a planar three-degree-of-freedom parallel manipulator with revolute joints. These networks rapidly learn complex nonlinear functions based on a database mapping. The networks learn the forward kinematics of the manipulator based on examples of the transformation. The obtained networks are then used to follow a test trajectory. For comparison purposes, a neural network approach using backpropagation is also used for this problem. The results show that, in this application, polynomial networks learn much faster and exhibit less error than neural networks.

Genetic algorithm for ellipsometric data inversion of absorbing layers

A new data reduction method is presented for single-wavelength ellipsometry. A genetic algorithm is applied to ellipsometric data to find the best fit. The sample consists of a single absorbing layer on a semi-infinite substrate. The genetic algorithm has good convergence and is applicable to many different problems, including those with different independent measurements and situations with more than two angles of incidence. Results are similar to those obtained by other inversion techniques.

Backlash elimination in parallel manipulators using actuation redundancy

In this work, accuracy enhancement through backlash elimination is considered. When a nonredundantly actuated parallel manipulator is subjected to a wrench while following a trajectory, required actuator torque switching (going from positive to negative or vice versa) may occur. If backlash is present in the actuation hardware for a manipulator, torque switching compromises accuracy. When in-branch redundant actuation is added, a pseudoinverse torque solution requires smaller joint torques, but torque switching may still occur. A method is presented where concepts of exploiting a nullspace basis of the joint torques are used to ensure that single sense joint torques can be achieved for the actuated joints. The same sense torque solutions are obtained using nonlinear optimization. The methodology is applied to several examples simulating parallel manipulators in machining applications.

Parallel manipulator kinematics learning using holographic neural network models

Abstract The forward kinematic problem of parallel manipulators is resolved using a holographic neural paradigm. In a holographic neural model, stimulus–response (input–output) associations are transformed from the domain of real numbers to the domain of complex vectors. An element of information within the holographic neural paradigm has a semantic content represented by phase information and a confidence level assigned in the magnitude of the complex scalar. Networks are trained on a database generated from the closed-form inverse kinematic solutions. After the learning phase, the networks are tested on trajectories which were not part of the training data. The simulation results, given for a planar three-degree-of-freedom parallel manipulator with revolute joints and for a spherical three-degree-of-freedom parallel manipulator, show that holographic neural network models are feasible to solve the forward kinematic problem of parallel manipulators.

A Comparison between Two Motion Planning Strategies for Kinematically Redundant Parallel Manipulators

In this work, a new approach for motion planning of kinematically redundant parallel manipulators is proposed and compared with a method previously proposed by the authors. First, motion planning is defined and thereafter overall motion planning (OMP) is introduced. OMP consists of determining actuation schemes that optimise the manipulator’s performance while considering the entire given trajectory of the end-effector at once. Next, the OMP method is compared to point-to-point motion planning. Two examples are given to compare the results of both methods. It is shown that the proposed OMP method can generate actuation schemes for given trajectories such that the manipulator avoids singular configurations.