📚 Reference

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Author： Jiewen Lai

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This repo contains the Matlab live script files (.mlx) that have been introduced in the following conference paper -

@inproceedings{lai2019learning,
  title={A learning-based inverse kinematics solver for a multi-segment continuum robot in robot-independent mapping},
  author={Lai, Jiewen and Huang, Kaicheng and Chu, Henry K},
  booktitle={Proc. IEEE Int. Conf. Robot. Biomim.},
  pages={576--582},
  year={2019},
}

The interactive live script helps one to understand better how the code works. It is only for verification/proof of concept.

I am using Matlab r2020a.

✔️ What is it about?

• This repo presents a simplified model to represent a multi-segment continuum robot using virtual rigid links. Based on the model, its IK can be solved using a multilayer perceptron (MLP) - a class of feedforward neural network (FNN).
• The transformation between virtual joint space to task space is described using Denavit-Hartenberg (D-H) convention.
• Using 20,000 established training data for supervised learning, the MLP reaches a mean squared error of 0.022 for a dual-segment continuum robot.
• The trained MLP is then used to find the joints for different end-effector positions, and the results show a mean relative error of 2.90% can be on the robot configuration.
• This simplified model and its MLP provide a simple method to evaluate the IK solution of a two-segment continuum robot, which can be further generalized and implemented in multi-segment cases.

👨‍💻 Try it yourself!

trainNetwork_DH.mlx:

• Compute the transformation matrix of a two-segment continuum robot based on the DH parameters (a virtual pseudo-rigid link model)
• Clear
• Based on the DH model, compute and save the IO relationship between the configuration ($R^4$) and tip cartesian ($R^6$).
• Train MLP

Calculation mode: MEX
 
Training Feed-Forward Neural Network with TRAINLM.
Epoch 0/5000, Time 0.508, Performance 15.7992/0, Gradient 57.1367/1e-07, Mu 0.001/10000000000, Validation Checks 0/10

Epoch 1/5000, Time 13.5, Performance 7.9875/0, Gradient 55.9948/1e-07, Mu 0.0001/10000000000, Validation Checks 0/10
Epoch 2/5000, Time 27.533, Performance 2.7576/0, Gradient 17.9319/1e-07, Mu 0.0001/10000000000, Validation Checks 0/10
Epoch 3/5000, Time 40.413, Performance 1.8418/0, Gradient 6.068/1e-07, Mu 0.0001/10000000000, Validation Checks 0/10
Epoch 4/5000, Time 51.652, Performance 1.2755/0, Gradient 3.5822/1e-07, Mu 0.0001/10000000000, Validation Checks 0/10
...
...
Epoch 71/5000, Time 830.364, Performance 0.013127/0, Gradient 0.18144/1e-07, Mu 1e-05/10000000000, Validation Checks 10/10
Training with TRAINLM completed: Validation stop.

• Save the network locally as ik_net.mat
• Test and show error

testPerformance.mlx:

• load ik_net.mat
• Use forward kinematics to compute the desired path
• Put the desired path as an input to the trained network -> get inverse output
• Use the inverse as new input, and test it forwardly
• Evaluate the error - you will see something like this (for example)

trainNetwork_DH_with_orientation.mlx - similar to the trainNetwork_DH.mlx but with orientaiton.

 

test_circle_hear.mlx - test file for trainNetwork_DH_with_orientation.mlx.

DH_para.mlx - symbolic calculation.