M. J. D. Hayes

On the kinematic constraint surfaces of general three-legged planar robot platforms

The variants of general three-legged planar robot platforms are enumerated and classified. Constraint surfaces corresponding to individual platform legs in the kinematic mapping image space are classified and parametrized. The parametric equations are free from representational singularities. The entire set consists of hyperboloids of one sheet and hyperbolic paraboloids. This result corrects an oversight in the body of literature. These surfaces have important applications to the kinematic analysis of planar three-legged robot platforms, hence appropriate attention should be given to their classification.

Unified Kinematic Analysis of General Planar Parallel Manipulators

A kinematic mapping of planar displacements is used to derive generalized constraint equations having the form of ruled quadric surfaces in the image space. The forward kinematic problem for all three-legged, three-degree-of-freedom planar parallel manipulators thus reduces to determining the points of intersection of three of these constraint surfaces, one corresponding to each leg. The inverse kinematic solutions, though trivial, are implicit in the formulation of the constraint surface equations. Herein the forward kinematic solutions of planar parallel robots with arbitral, mixed leg architecture are exposed completely, and in a unified way, for the first time. Copyright

Pareto Optimality and Multiobjective Trajectory Planning for a 7-DOF Redundant Manipulator

This paper presents a novel approach to solve multiobjective robotic trajectory planning problems. It proposes to find the Pareto optimal set, rather than a single solution usually obtained through scalarization, e.g., weighting the objective functions. Using the trajectory planning problem for a redundant manipulator as part of a captive trajectory simulation system, the general discrete dynamic programming (DDP) approximation method presented in our previous work is shown to be a promising approach to obtain a close representation of the Pareto optimal set. When compared with the set obtained by varying the weights, the results confirm that the DDP approximation method can find approximate Pareto objective vectors, where the weighting method fails, and can generally provide a closer representation of the actual Pareto optimal set.

Solving the forward kinematics of a planar three-legged platform with holonomic higher pairs

A practical solution procedure for the forward kinematics problem of a fully-parallel planar three-legged platform with holonomic higher pairs is presented. Kinematic mapping is used to represent distinct planar displacements of the end-effector as discrete points in a three dimensional image space. Separate motions of each leg trace skew hyperboloids of one sheet in this space. Therefore, points of intersection of the three hyperboloids represent solutions to the forward kinematics problem. This reduces the problem to solving three simultaneous quadratics. Applications of the platform are discussed and an illustrative numerical example is given.

Solving the Burmester Problem Using Kinematic Mapping

Planar kinematic mapping is applied to the five-position Burmester problem for planar four-bar mechanism synthesis. The problem formulation takes the five distinct rigid body poses directly as inputs to generate five quadratic constraint equations. The five poses are on the fourth order curve of intersection of up to four hyperboloids of one sheet in the image space. Moreover, the five poses uniquely specify these two hyperboloids. So, given five positions of any reference point on the coupler and five corresponding orientations, we get the fixed revolute centres, the link lengths, crank angles, and the locations of the coupler attachment points by solving a system of five quadratics in five variables that always factor in such a way as to give two pairs of solutions for the five variables (when they exist).Copyright

A Simple, Low Cost, 3D Scanning System Using the Laser Light-Sectioning Method

The use of 3D scanning systems for acquiring the external shape features of arbitrary objects has many applications in industry, computer graphics, and more recently, the biomedical field. The potential exists to expand the use of 3D models even further, by continuing to develop simpler, more cost effective systems. A simple, lost cost, 3D scanning system is presented which employs a laser light-sectioning technique. Results of a proof of concept experiment for the proposed system demonstrate the validity of the chosen approach. Directions for future work are also discussed.

Localization in large-scale underground environments with RFID

Localization using satellite-based GPS is not available in underground mines, therefore a new approach is required. This paper presents a method for localizing a sensor-equipped vehicle in a large-scale underground environment by using a particle filter and a collection of 2D a priori node maps. Sporadically placed passive RFID tags are used in the creation of the locally consistent node maps and for helping to solve the global localization problem. Experimental results from realtime localization in the multi-kilometre Carleton University underground tunnels are presented.

A 3D scanning system for biomedical purposes

The use of three-dimensional (3D) scanning systems for acquiring the external shape features of biological objects has recently been gaining popularity in the biomedical field. A simple, low cost, 3D scanning system is presented, which employs the laser light-sectioning technique for data acquisition. A Direct Linear Transformation least squares algorithm is used for camera calibration and Elliptical Fourier Descriptors (EFDs) are used for data smoothing and planar section reconstruction. Results for an experiment demonstrating the validity of the EFD approach are presented. Overall, results presented for three objects scanned with the proposed system demonstrate the validity of the chosen approach. This is an expanded version of a paper presented at the 3rd IEEE International Workshop on Medical Measurements and Applications, 9 10 May 2008, Ottawa, ON, Canada.

A Dynamic Programming Approach to Redundancy Resolution with Multiple Criteria

This paper studies the problem of generating optimal joint trajectories for redundant manipulators when multiple criteria need to be considered and proposes a novel approach based on dynamic programming and the use of the Pareto optimality condition. The drawbacks of the traditional weighting method in optimization for generating the Pareto optimal set are discussed and an alternate approach using dynamic programming is proposed. The two approaches are implemented on the model of a 7-DOF redundant manipulator with the end-effector moving along a prescribed trajectory, while the joint trajectories are required to minimize two particular criteria. The results illustrate that the dynamic programming approach provides a better approximation of the Pareto optimal set and a more flexible and predictable framework to control the objective vectors.

Unified Treatment of the Kinematic Interface Between a Sphere and Omnidirectional Wheel Actuators

This paper presents a general approach to the kinematics of an orientation motion platform utilizing a sphere actuated by omnidirectional wheels. The number and type of the omnidirectional wheels, as well as their position and orientation relative to the sphere are arbitrary, provided they are distinct. In this paper, the general kinematics are presented and illustrated by sample configurations with a range of omnidirectional wheel types and quantities. Moreover, no-slip conditions are identified, and the resulting expressions and their implications on the design of such a mechanical system are demonstrated by means of several benchmark examples.