ROC-HJ solver: Reachability and Optimal Control software

This is a C++ software for solving some HJB equations arising in reachability analysis and control theory.


The software ROC-HJ is a C++ precompiled library that implements a set of numerical methods for solving some Hamilton-Jacobi equations arising in optimal control theory. The library also contains some useful tools for analyzing the numerical solutions and aiming at designing the optimal control laws along with the corresponding optimal trajectories.
The code can run for any dimension d≥1 limited only by the machine capacity. The library can be used for a large class of deterministic control problems including: reachability analysis, path planning, collision avoidance, infinite horizon control problems, minimum time problems, Mayer or Bolza type problem, state-constrained control problems, differential games, exit time problems.

 For more details, click here !



 C++ software

The library was precompiled and tested on three target systems: Windows, LINUX and MacOS. In all cases, the library requires some building tools for C/C++ installed on the computer:

  • CMake Build chain ( available for all systems at
  • GCC compiler (native for LINUX and Mac OS, MINGW distribution for Windows :

Some basic knowledge of C programming syntax is necessary to describe a new problem to be solved by the HJB-Solver. For more details, see the pdf file here.


Select the file according to your operating system from the following list to get the latest version for your computer:  Linux 32-bit  or 64-bit;  Mac OS 64-bit; Windows



To illustrate different numerical methods implemented in the ROC-HJ library some control problems were considered and for each example a Graphical User's Interface is proposed. It allows to define the parameters of each model and of the numerical method used to solve it.  

  • Zermelo's Navigation problem: reachability analysis under state constraints, minimum time function, reconstruction of optimal trajectories
  •  Dubin's car problem: reachability analysis, minimum time function, reconstruction of optimal trajectories
  • Advection-rotation HJ equation: comparison of different numericla methods for solving a linear HJ equation
  • Unsafety regions: collision avoidance for  UAVs

 The graphical interfaces are developed with MATLAB and require a MATLAB licence to run.

To download the examples, select your computer operating system: Linux, Mac OS, Windows


Prof. Hasnaa Zidani or Prof. Olivier.Bokanowski 






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