A python based system for generating closed-form solutions to the manipulator inverse kinematics problem using behavior trees for action selection. Solutions are fully symbolic and are output as LaTex, Python, and C++.
- New feature: Can generate python code for Forward Kinematics only. This code can be sub-optimal, and equations can be over complex when the alpha parameter is not a nice multiple of pi/2 (sin(al) != {0,1}). This is the case for a few robots like Raven-II. Now in this case constants with the sine and cosine values of alpha are automatically created and swapped in to the FK equations. Generated code initializes the new constants. Try >python3 fkOnly <RobotName>. Output is in the CodeGen directory.
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Release v2.2 has refactored one of the more arcane solution nodes (x2y2solver) so that it instead transforms the equation for later solution by any solver. KawasakiRS007L can now be solved! (Still an obscure bug with sum-of-angle substitution, see commends in ik_classes.py)
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Latex output has been refactored. New Latex procedure is simplified as follows:
- run IKBT
- cd LaTex
- pdflatex ik_solutions_ROBOTNAME.tex
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A new top-level is provided to do Forward Kinematics and Jacobian matrix only.
- python fkOnly.py ROBOTNAME
- cd LaTex
- pdflatex fk_equations_ROBOTNAME.tex
We've accumulated experience from many installations with the help of students in ECE 543 (University of Washington). One issue that came up is that with python 3.6.X something fails in the complex graph of imports. This works fine with python 3.8.X. We haven't attempted to fix this.
Recent commits to main have corrected some remaining python 2 hangovers in Latex outout and python output (even python 3 code can generate pytyon 2 print statements!).
At long last the 3-way sum of angles feature is upgraded to python3 and merged into main branch. All tests are passing, UR5 and Puma both solve all unknowns. USE MAIN BRANCH.
Unit test programs were broken for python3. This is now fixed. Test programs work and all pass.
Upgraded to Python3 (mostly just adding parens to print statements and new python3-sympy). New "main" branch for more respectful terminology.
BH has fixed the UR5 regression - it now works again and solution output no longer shows sum-of-angles variables that are not needed in the actual solution.
Use branch RepairUR5Regression for latest and greatest version.
BH has fixed the UR5 regression - it now works again and solution output no longer shows sum-of-angles variables that are not needed in the actual solution.
Use branch RepairUR5Regression for latest and greatest version.
Work aimed at #15 and #18 is still ongoing (it's tough!). But a few smaller bugs have been fixed which are now in the 'testing' branch. Please try that branch and post issues. THX.
BH is working on a new implementation of the solution graph and generating the list of solutions (much trickier that it seems at first!). I've taken this work to a private repo fork to decluter this page, but will merge and commit shortly. This work is aimed at issues #15 and #18. Thanks to you new issue posters!
Sum-of-Angles transform now works for the case of three angles (corresponds to three parallel axes in the mechanism). IKBT can now solve the UR5 and similar robots!
- We built an autonomous inverse kinematics solver (IKBT) using a behavior tree to organize solution algorithms.
- We incorporated knowledge frequently used (by human experts) when solving inverse kinematics into a behavior tree. These rule-based solvers applicable to any serial-chain, non-redundant, robot arm.
- IKBT generates a dependency {\it graph} of joint variables after solving, generating all possible solutions.
- IKBT provides convenience features such as automatic documentation of the solution in \LaTeX and automatic code generation in Python and C++.
- Implementation in a modern open-source, cross-platform, programming language (Python) with minimal dependencies outside of the standard Python distribution ({\tt sympy}).
- Introductory Video (6min)
- How to set up IKBT for your own robot arm (6.5min)
Zhang, Dianmu, and Blake Hannaford. "IKBT: solving symbolic inverse kinematics with behavior tree." Journal of Artificial Intelligence Research 65 (2019): 457-486. Link
Zhang, Dianmu, and Blake Hannaford. "IKBT: solving closed-form Inverse Kinematics with Behavior Tree." arXiv preprint arXiv:1711.05412 (2017). Link
You need the following to be installed to run IKBT:
- Python 3.8.x (Python Installation)
- Sympy python package (Installation instructions for all OS)
- Latex package (for nice equation output - highly recommended) (Install Latex)
A list of all DH parameters tested in the paper: ['Puma', 'Chair_Helper', 'Wrist', 'MiniDD', 'Olson13','Stanford', 'Sims11', 'Srisuan11', 'Axtman13', 'Mackler13', 'Minder13', 'Palm13', 'Parkman13', 'Frei13', 'Wachtveitl', 'Bartell', 'DZhang', 'Khat6DOF'.]
We suggest you first run the Wrist since it is relatively fast:
python ikSolver.py Wrist
To solve your own problem open the file ikbtfunctions/ik_robots.py and create an entry for your robot. You should copy an entry for an existing robot and edit it's entries. Create an "unknown" for each joint variable and package them into the vector "variables". Enter the DH parameters in matrix form. Also, enter the name of your robot into the list of valid names (ikbtfunctions/ik_robots.py, line 31).
DH parameters explained: The vector "vv" encodes whether each joint is rotary (1) or prismatic (0). If your robot is less than 6 DOF, create empty rows: [ 0 , 0, 0, 0 ], in the DH table so that it has six rows. Many standard symbols in robot kinematics are pre-defined for you but if you use any new ones, be sure to define them using sp.var(). See "Wrist" for an example in which the three joint variables "A, B, C" are set up for sympy by sp.var('A B C'). "pvals" is where you can put in the numerical values for all parameters, for result verification purposes.
Pre-computed forward kinematics.
Sometimes computation of the forward kinematic equations (and their subsequent simplification) can be time consuming. When debugging an inverse kinematics solution (for example modifying the BT), it can slow the cycle if these have to be redone each time. Therefore, the software has a mechanism using Python "pickle" files, to cache the forward kinematics computation and not repeat it. Forward kinematics pickle files are stored in the directory fk_eqns/. This directory will be automatically created if you don't have it. In some cases you may have to delete the pickle file for your robot. To do that, >rm fk_eqns/NAME_pickle.p. IKBT will generally tell you when you should do this, but it is OK to just >rm -rf fk_eqns/ .
