Cassie Gait Library Optimization using C-FROST

This repository contains an example using C-FROST to generate a library of walking gaits for Cassie series robot. The code depends on FROST and C-FROST. The Cassie model used in this example can be found here. These dependant packages are also included as git submodules for convenience.

This example has been tested on Ubuntu 16.04 and Windows Subsystem on Linux (WSL).

Download

To download this example with submodules, run:

cd ~
git clone --recursive [email protected]:UMich-BipedLab/Cassie_CFROST.git

After download, you should set up FROST and C-FROST accordingly. For more information, see

• FROST Installation
• C-FROST Installation

Generate necessary functions

To run the optimization using C-FROST, first needs to set up the problem in MATLAB using FROST and generate all required functions. In this example, we put functions for system dynamics into a separate directory, and compile them as a static library that can be linked to the main optimization problem. This way, you do not need to re-compile these functions every time after you change the optimization constraints.

Generate functions for system dynamics

First, run gen_lib.m script in MATLAB. This process may take a while to finish. By default, we drop the velocity terms ($C(q)\dot{q}$) from the dynamics equation. To include them, set OMIT_CORIOLIS to false in gen_lib.m script, and re-run the script. After successfully run the script in matlab, you should find three new directories, src, include, and mex.

In terminal, run the following to compile the static library:

cd ~/Cassie_CFROST/Cassie_Example/cassie_dynamics-library
mkdir build
cd build
cmake ..
make
make install

The last command will move the compiled library libcassie_dynamics.a to the lib folder.

Generate other functions and optimization configuration files

Next, run cassie_opt.m script in MATLAB to generate other functions and configuration files. This script should create two folders:

• gen: export and compile MEX binaries used for FROST in MATLAB (you can run the optimization in MATLAB as before)
• periodic: export all functions and configuration files required for C-FROST.

For detailed process of generating these files, please refer to the comments in the script.

Compile C-FROST program

In terminal

cd ~/Cassie_CFROST/Cassie_Example/opt_two_step/periodic/c_code
mkdir build
cd build
cmake ..
make
make install
cd ..

This will compile the C-FROST optimization problem to an executable called program in the folder periodic/c_code. To run the program, run:

./program --initial 'res/init.json' --options '../ipopt.opt' --data 'res/data.json' --bounds 'res/bounds.json' --solution '../local/output/sol.json'

The input arguments are:

• --initial: the JSON file that stores the initial guess of the optimization
• --options: the option file (with extension .opt) for IPOPT
• --data: the JSON file that describe the problem structure
• --bounds: the JSON file that stores boundary values of optimization variables and constraints
• --solution: the output file to export the optimization results (structured data, more information)
• --output: another output file to export the optimization results (just the vector of solution from IPOPT)

C-FROST will export the optimization results to the specified JSON file. This can be easily imported to MATLAB to further analyze the optimal gait. A simple example of loading this file, see analyze_solution.m.

Run multiple gait optimization

With C-FROST, it is easy to run multiple gait optimization in parallel. You do not need to recompile the program as long as these optimizations use the same problem strcuture (same set of variables, constraints and cost functions). To run multiple optimization with different bounds, you would need to generate the bound JSON files for all optimization a priori.

In this example, we generate 11x11x11=1,331 gaits with different walking speeds and ground inclinations. This can be done by changing the constraints bounds in the same optimization problem.

In MATLAB, run generate_multiple_bounds.m script to generate all bound files first. The process may take a while to finish.

Once done, you can use run multiple optimization in parallel from the terminal. We particularly use GNU Parallel package for this process.

parallel ./program --initial 'res/init.json' --options '../ipopt.opt' --data 'res/data.json' --bounds "res/bounds_{}.json" --solution "../local/output/sol_{}.json" ">" "../local/log/log_{}.txt" ::: {1..1331}

You can use time to measure the run time:

time parallel ./program --initial 'res/init.json' --options '../ipopt.opt' --data 'res/data.json' --bounds "res/bounds_{}.json" --solution "../local/output/sol_{}.json" ">" "../local/log/log_{}.txt" ::: {1..1331}

The optimization results will be saved to local/output/ folder, and the terminal outputs will be save to local/log folder. The scripts export_all_gaits.m and check_logs.m can be used to import the resuls into MATLAB and check the log files.