{"source":"G. Giacomuzzo, A. Dalla Libera (University of Padua), D. Romeres (Mitsubishi Electric Research Laboratories, MERL), data of 'A Black-Box Physics-Informed Estimator Based on Gaussian Process Regression for Robot Inverse Dynamics Identification', 2024, Zenodo 10.5281/zenodo.12516500, Franka Emika Panda, real robot","license":"CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/). Adapted: every 3rd sample of the trajectories, rounded; the nominal-model torque and NAI-fnet's predictions 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0.519·(√(√(√(hinge(q̇₄)))))","− 0.109·(cos q₄ − hinge(sin q₃))","+ 0.158·(sin q₂)","− 0.0123·(q₅)","+ 0.0557·(cos q₇)","+ 0.00761·(q̈₃)","+ 0.00666·(q̈₅)","− 0.166·(√(hinge(−q̇₄)))","− 0.00647·(q̈₂)","− 0.16·(sin q₄)","− 0.0134·(q̈₄)","− 0.0715·(cos q₃)"],"best":12},"code":{"bytes":33824,"ns":646,"lines":["#include <math.h>","","/* part of the model: its neurons, as formulas */","static double fnet_core0(const double x[35]) {","    double s = (double)0.37351673900124743;","    s += (double)0.51908212276103904 * sqrt(sqrt(sqrt(fnet_hinge_d(x[10]))));","    s += (double)-0.10870883806701505 * (x[31] - fnet_hinge_d(x[23]));","    s += (double)0.15797843735074976 * x[22];","    s += (double)-0.01230066208022406 * x[4];","    s += (double)0.055716649969486616 * x[34];","    s += (double)0.007614945134597908 * x[16];","    s += (double)0.0066639006643078105 * x[18];","    s += (double)-0.16558470672218178 * sqrt(fnet_hinge_d((-x[10])));","    s += (double)-0.0064748725626761006 * x[15];","    s += (double)-0.16006778427022469 * x[24];","    s += (double)-0.013372094519342301 * x[17];","    s += (double)-0.071476869033755872 * x[30];","    return s;","}","","/* ... the rest of the model ... */","","FNET_REAL fnet_predict(const FNET_REAL xin[]);","FNET_REAL fnet_predict(const FNET_REAL xin[]) { /* ... */ 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· Record","body":"In the lab the arm runs an excitation motion: sums of sines in every joint. The decision centre logs the 7 joint angles, their speeds and accelerations, and the elbow torque from a reference sensor that the android will not carry. Two recorded trajectories, every 10th sample: <b>586 rows</b>, 21 inputs."},"train":{"title":"2 · Train","body":"On a PC, NAI-fnet grows a network for what the robot's nominal model gets wrong, one neuron at a time; each neuron is a short formula. Growth stops at <b>12 neurons</b>, when the next one no longer pays for itself."},"flash":{"title":"3 · Flash","body":"The model becomes plain C: <b>33,824 bytes</b> of code and constants, no runtime, no dynamic memory. It goes into the elbow's microcontroller; the compiled code gives the model's numbers bit for bit."},"run":{"title":"4 · Run","body":"A trajectory the model has never seen. Every cycle the chip takes the arm's state from the bus and returns the torque the elbow must give: <b>nMSE 0.077 %</b> on this run, against 0.72 % for the nominal model alone. Push the arm: a gap between measured and predicted torque above 0.8 N·m for 0.2 s means contact (the rule is set on recorded trajectories this page does not show). The nominal model alone needs 1.6 N·m and misses a 1.25 N·m push."}}}