Dynamic Game SQP

Author: Edward Zhu (edward.zhu@berkeley.edu)

This repository contains a Python implementation of the Dynamic Game SQP algorithm.

Related Papers

• Zhu, Edward L., and Francesco Borrelli. "A sequential quadratic programming approach to the solution of open-loop generalized nash equilibria." 2023 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2023. arXiv
• Zhu, Edward L., and Francesco Borrelli. "A Sequential Quadratic Programming Approach to the Solution of Open-Loop Generalized Nash Equilibria for Autonomous Racing." arXiv preprint arXiv:2404.00186 (2024). (Under review). arXiv, data

Installation

Dependencies:

• numpy
• scipy
• casadi
• osqp
• matplotlib

The following command will install the Python package DGSQP:

python3 -m pip install -e .

Installing the CPLEX QP solver for DGSQP

CPLEX is a QP, LP, and mixed integer solver developed and maintained by IBM and is provided as a part of IBM ILOG CPLEX Optimization Studio. Academic users are allowed free access to the solver after registering for an account. To use CPLEX with CasADi Python:

1. Download ILOG CPLEX Optimization Studio according to https://ronennir.medium.com/installing-cplex-optimization-studio-on-ubuntu-20-04-53e234ca4ec2.
2. Install CPLEX using sudo (this will default to /opt/ibm/ILOG on Ubuntu).
3. Copy the compiled CPLEX library (found at /opt/ibm/ILOG/CPLEX_Studio<CPLEX_VERSION>/cplex/bin/x86-64_linux/libcplex<CPLEX_VERSION>.so), to the CasADi Python package installation directory:
   • Local installation: ~/.local/lib/python3.8/site-packages/casadi
   • Global installation: /usr/local/lib/python3.8/site-packages/casadi
4. Before creating the solver (e.g. using ca.conic), set the system environment variable CPLEX_VERSION to match the version of the solver that you have installed (e.g. using os.environ['CPLEX_VERSION']='2210' for v22.1.0).
5. Set the parameter DGSQPV2Params.qp_solver = 'cplex'

Installing the PATH solver

To run the comparisons using the PATH solver, install the prerequisites using the following steps

1. Install Julia:

• wget https://julialang-s3.julialang.org/bin/linux/x64/1.10/julia-1.10.1-linux-x86_64.tar.gz
• tar zxvf julia-1.10.1-linux-x86_64.tar.gz
• export PATH="$PATH:/path/to/<Julia directory>/bin"

2. Install Julia packages:

• In the Julia REPL package manager:
• add PyCall
• add PATHSolver@1.1.1
• (note, only version 1.1.1 works when called from pyjulia)

3. Install pyjulia:

• python3 -m pip install julia

Quick Start

Scripts for running the experiments presented in the paper can be found in the scripts directory.