Neural kinematic modelling
Centre for Systems and Control, IIT Bombay · 2026
Under review, Indian Control Conference
Abstract
A five-segment tendon-driven continuum arm has no closed-form kinematics. The shape it takes is set by the deformation of the structure itself, and the inverse mapping is one-to-many. Both directions are learned from Qualisys motion capture, with the inverse treated as a distribution over configurations rather than a single answer.
Why analytical kinematics does not apply
Rigid-link manipulators have kinematics you can derive. This arm is five continuum segments actuated by four tendons in a plus configuration, driven by two differential motors. The pose it reaches under a given actuation depends on how the structure deforms, and several distinct configurations place the tip at the same point.
Forward model
A two-layer LSTM over a five-step window of actuation history predicts tip position and orientation. Giving it recent history rather than the instantaneous command lets the deformation state of the structure inform the prediction.
Orientation is handled with a quaternion-aware geometric loss rather than a naive regression on quaternion components, and the training set is augmented by spherical linear interpolation between measured poses.
Inverse model
The inverse model is a mixture density network with eight components, conditioned on the current and previous pose along with the previous actuation. Regressing a single output for a one-to-many map averages across valid solutions and lands between them, on a configuration that is not valid at all. Predicting a mixture keeps the modes separate.
Evaluation
Ground truth comes from Qualisys motion capture across five rigid-body markers on the arm. Accuracy is reported as spatial position error in millimetres and geodesic angular error, rather than a single averaged loss that would hide which of the two is failing.