Algebraic-elimination based solution of inverse kinematics for a humanoid robot finger

A cortically-inspired model for inverse kinematics computation of a humanoid finger with mechanically coupled joints

“…The findings suggest that our cortical model could be used effectively as a neurorobotic controller for overt/ covert finger motion, computing accurate, robust and flexible inverse kinematics for the control of humanoid robotic hand/fingers. Previous studies have suggested that the computation of the inverse kinematics including linear and nonlinear coupled joints is particularly challenging (Collins 2003, Jiang et al 2007, Jiang et al 2009, Godler et al 2010, Lin et al 2011. In order to solve this inverse kinematic problem with coupled joints, several proposed approaches were based on analytical solutions that depend on numerical constraints combined with look-up table (e.g., Jiang et al 2007, Jiang et al 2009 and numerical interpolation (e.g., Jiang et al 2007, Jiang et al 2009, Lin et al 2011 without the ability to adapt to task demands and/or environmental constraints.…”

“…Previous studies have suggested that the computation of the inverse kinematics including linear and nonlinear coupled joints is particularly challenging (Collins 2003, Jiang et al 2007, Jiang et al 2009, Godler et al 2010, Lin et al 2011. In order to solve this inverse kinematic problem with coupled joints, several proposed approaches were based on analytical solutions that depend on numerical constraints combined with look-up table (e.g., Jiang et al 2007, Jiang et al 2009 and numerical interpolation (e.g., Jiang et al 2007, Jiang et al 2009, Lin et al 2011 without the ability to adapt to task demands and/or environmental constraints. For instance, Godler et al (2010) proposed an algebraic solution of the inverse kinematics for a robotic finger with two joints linearly coupled.…”

“…From a biomechanical modelling perspective, in an attempt to achieve comparable performance to that observed with human hands/fingers and to enhance human-robot interactions, over the last decade the field of humanoid robotics has proposed various artificial anthropomorphic fingers/hands that are biomechanically inspired by humans (e.g., Lovchik and Diftler 1999, Butterfass et al 2001, Akin et al 2002, Kawasaki et al 2002, Zollo et al 2007, Paik et al 2012, Karnati et al 2013, Mattar 2013, Kent and Engeberg 2014. Although these versatile multi-fingered humanoid hands are expected to outperform simple grippers by performing fine and complex tasks, they require a complex kinematic system to control (e.g., Yoshikawa 2010, Lin et al 2011). In most recently developed humanoid robotic hands (e.g., Robonaut…”

“…The mechanical coupling between two joints means that one joint moves as a function of the other. Thus, the inverse kinematics problem becomes particularly challenging since it involves transcendental equations that cannot be solved algebraically, and solving it generally requires specific conditions and assumptions (Collins 2003, Jiang et al 2007, Jiang et al 2009, Godler et al 2010, Lin et al 2011.…”

“…The first one includes models that do not account for any particular neurophysiological substrate, leading to very limited or even no biological plausibility (e.g., Oyama et al 2001). As with the previously mentioned analytical solutions, such non-biological neural models used as inverse kinematic controllers did not consider the embodiment of human sensorimotor processes such as covert performance through sensorimotor predictions for fine control of finger motion (e.g., Oyama et al 2001, Collins 2003, Jiang et al 2007, Jiang et al 2009, Godler et al 2010, Lin et al 2011.…”