Asymmetric Dual-Arm Task Execution using an Extended Relative Jacobian

Coordinated dual-arm manipulation tasks can be broadly characterized as possessing absolute and relative motion components. Relative motion tasks, in particular, are inherently redundant in the way they can be distributed between end-effectors. In this work, we analyse cooperative manipulation in terms of the asymmetric resolution of relative motion tasks. We discuss how existing approaches enable the asymmetric execution of a relative motion task, and show how an asymmetric relative motion space can be defined. We leverage this result to propose an extended relative Jacobian to model the cooperative system, which allows a user to set a concrete degree of asymmetry in the task execution. This is achieved without the need for prescribing an absolute motion target. Instead, the absolute motion remains available as a functional redundancy to the system. We illustrate the properties of our proposed Jacobian through numerical simulations of a novel differential Inverse Kinematics algorithm.Comment: Accepted for presentation at ISRR19. 16 Page

Regression with Distance Matrices

Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which requires only the specification of a distance function. A low-dimensional representation of such distance matrices can be obtained using methods such as multidimensional scaling. Once these variables have been represented as scores, an internal model linking the predictors and the response can be developed using standard methods. We call scoring the transformation from a new observation to a score while backscoring is a method to represent a score as an observation in the data space. Both methods are essential for prediction and explanation. We illustrate the methodology for shape data, unregistered curve data and correlation matrices using motion capture data from an experiment to study the motion of children with cleft lip.Comment: 18 pages, 7 figure