Distributed Inverse Kinematics for Shape-changing Robotic Materials

We present a distributed algorithm to calculate inverse kinematic solutions for shape-changing beams with integrated sensing, actuation, computation and communication. We consider the beam to consist of n segments that can each change their curvature, perform computation and communicate with their neighbors. Using a centralized inverse Jacobian method this solution has a computational complexity of (n2.373) as it relies on matrix inversion. We describe the system as a kinematic chain and derive a distributed algorithm for computing its inverse kinematics. The presented method distributes the computation among the n segments by sequentially applying the inverse Jacobian method to m-segment neighborhoods, reducing the computational complexity of each individual operation to m3) at the expense of mn) communication exchanges and solving the reduced problems ) times across the length of the beam. The resulting solution does not require any external computation and can autonomously calculate a curvature profile to reach a desired end-pose, which has applications ranging from adaptive aerodynamic surfaces to smart furniture. The proposed algorithm has been validated using computer simulations of beams with up to 30 elements and various neighborhood sizes. Results show that the proposed approach allows trading accuracy and converge rate with increasing computation and communication.