ML for Finite Element Analysis and Inverse Kinematics

BLUF - Here, I trained and tested two ML models to generate stress profiles of varying shapes and positional goals for robot arms.

Large datasets sampled from the real world or synthetic power machine learning. A basic model of machine learning (ML), known as a fully connected or multi-layer perceptron (MLP), can serve as a universal function approximator. Quantities like stress distributions in a planar object or joint angles for a robotic arm can be accurately computed with MLPs of sufficient size and generalizable here. Where traditional software algorithms following closed-form functions or iterative methods may require inaccessibly difficult mathematical intuition and a thorough, rational process, ML models skip the analysis by automatically finding relationships between variables to directly generate a result. Using ML, results can be found for out-of-distribution inputs or finding the best output among infinite solutions.

Finite Element Analysis (FEA) Data Acquisition

For the FEA samples, data was generated from a FEA software that discretized the 100 planar shapes into nodes and computed their stresses at each colored location. Each shape is subject to an identical load in the plane.

FEA Model Initialization

The neural network model that performed FEA consisted of five hidden layers [64,80,80,64,32] , without any dropout, Xavier initialization, or batch normalization. Hyperbolic tangent activation functions interweave each layer.

Model Training

An 80/20 split was used for training and testing. A feed forward neural network learned the way stress is distributed based on geometry and load, converging to a stably low error.

Model Results

Convergence on loss without oscillations indicates that the model has learned the relationship between load, boundary conditions, part geometry, and material properties

Model Results

Plotting the R-squared value shows that the model predicts stress well, giving a value of 0.8728

IK Data Acquisition

For the IK samples, 10000 data points consisting of locations in a 2D grid for the robot to achieve with its end effector, were synthetically sampled.

IK Model Initialization

Three total architectures for the IK were tested, with one hidden layer of 12 perceptrons [12], two layers of 24 perceptrons each [24,24], and three hidden layers of 48 perceptrons each [48,48,48]. ReLU activation functions succeed each layer except for the output.

IK Model Training

Similarly, another neural network learned which values to assign joint parameters to achieve high accuracy of desired end positions.

IK Model Prediction

With increasing model complexity, the order of magnitude of error decreased by one when increasing the number of neurons by polynomial factor. A neural network of [12] yielded 8.6e-3, [24,24] yielded 1.3e-3, and [48,48,48] yielded 2.4e-4.

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