Kinematic Parameter Estimation Using Workspace Manifold Mapping

This work proposes a method to estimate the kinematic parameters of multi-joint systems where direct measurement is infeasible, such as joints of the hand.

Our novel data-driven estimation method uses "workspace manifold mapping" that relies on a unique geometry that arises in exponential representations of 3D motions of two rigid bodies connected via one- or two-degree-of-freedom (DOF) joints. We describe and verify our "Generative Topographic Mapping algorithm with kinematic constraints" (GTM-KC) using simulated data and motion capture data for a 2-DOF bio-inspired mechanical linkage. We compare the performance of GTM-KC to several benchmark algorithms.

Upon applying GTM-KC to motion capture data of a bio-inspired linkage, the mean estimates of the 2-DOF joint axis orientations deviated from ground truth by 2.5° with a standard deviation of 3.4° for one axis and by 2.4° with a standard deviation of 2.7° for the second axis.

Our GTM-KC method can be used to estimate the orientations of revolute joint axes that link the 3D kinematics of two rigid bodies, and either outperforms or is equivalent to existing methods in terms of accuracy, precision, and reliable convergence to a solution. Notably, the GTM-KC method outperforms existing methods in terms of robustness to initial conditions.

Workspace manifold mapping provides improved kinematic parameter estimation as compared to existing benchmark methods, and can be applied to any 1- or 2-DOF kinematic relationship without loss of generality.