Code samples#

MuJoCo comes with several code samples providing useful functionality. Some of them are quite elaborate ( in particular) but nevertheless we hope that they will help users learn how to program with the library.


This code sample tests the simulation speed for a given model. The command line arguments are the model file, the number of time steps to simulate, the number of parallel threads to use, and a flag to enable internal profiling (the last two are optional). When N threads are specified with N>1, the code allocates a single mjModel and per-thread mjData, and runs N identical simulations in parallel. The idea is to test performance with all cores active, similar to Reinforcement Learning scenarios where samples are collected in parallel. The optimal N usually equals the number of logical cores. By default the simulation starts from the model reference configuration qpos0 and qvel=0. However if a keyframe named “test” is present in the model, it is used as the initial state state.

The timing code is straightforward: the simulation of the passive dynamics is advanced for the specified number of steps, while collecting statistics about the number of contacts, scalar constraints, and CPU times from internal profiling. The results are then printed in the console. To simulate controlled dynamics instead of passive dynamics one can either install the control callback mjcb_control, or set control signals explicitly as explained in the simulation loop section below.


This code sample tests the parser, compiler and XML writer. The testing code does the following:

  • Parse and compile a specified XML model in MJCF or URDF. This yields an mjModel structure ready for simulation;

  • Save the model as a temporary MJCF file, using a “canonical” subset of MJCF where a number of conversions have already been performed by the compiler;

  • Parse and compile the temporary MJCF file. This yields a second mjModel structure ready for simulation;

  • Compare the two mjModel structures field by field, and print the field with the largest numerical difference. Since MJCF is a text format, the real-valued numbers saved in it have lower precision than the double precision used internally, thus we cannot expect the two models to be identical on the bit level. But we can expect the largest difference to be on the order of 1e-6. A substantially larger difference indicates a bug in the parser, compiler or XML writer - and should be reported.

The code uses the X Macros described in the Reference chapter. This is a convenient way to apply the same operation to all fields in mjModel, without explicitly typing their names. The code sample also uses X Macros to implement a watch, where the user can type the name of any mjData field which is resolved at runtime.


This code sample evokes the built-in parser and compiler. It implements all possible model conversions from (MJCF, URDF, MJB) format to (MJCF, MJB, TXT) format. Models saved as MJCF use a canonical subset of our format as described in the Modeling chapter, and therefore MJCF-to-MJCF conversion will generally result in a different file. The TXT format is a human-readable road-map to the model. It cannot be loaded by MuJoCo, but can be a very useful aid during model development. It is in one-to-one correspondence with the compiled mjModel. Note also that one can use the function mj_printData to create a text file which is in one-to-one correspondence with mjData, although this is not done by the code sample.


This code sample is a minimal interactive simulator. The model file must be provided as command-line argument. It opens an OpenGL window using the platform-independent GLFW library, and renders the simulation state at 60 fps while advancing the simulation in real-time. Press Backspace to reset the simulation. The mouse can be used to control the camera: left drag to rotate, right drag to translate in the vertical plane, shift right drag to translate in the horizontal plane, scroll or middle drag to zoom.

The Visualization programming guide below explains how visualization works. This code sample is a minimal illustration of the concepts in that guide.


This code sample is a fully-featured interactive simulator. It opens an OpenGL window using the platform-independent GLFW library, and renders the simulation state in it. There is built-in help, simulation statistics, profiler, sensor data plots. The model file can be specified as a command-line argument, or loaded at runtime using drag-and-drop functionality. As of MuJoCo 2.0, this code sample uses the native UI to render various controls, and provides an illustration of how the new UI framework is intended to be used. Below is a screen-capture of simulate in action:

Interaction is done with the mouse; built-in help with a summary of available commands is available by pressing the F1 key. Briefly, an object is selected by left-double-click. The user can then apply forces and torques on the selected object by holding Ctrl and dragging the mouse. Dragging the mouse alone (without Ctrl) moves the camera. There are keyboard shortcuts for pausing the simulation, resetting, and re-loading the model file. The latter functionality is very useful while editing the model in an XML editor.

The code is quite long yet reasonably commented, so it is best to just read it. Here we provide a high-level overview. The main() function initializes both MuJoCo and GLFW, opens a window, and install GLFW callbacks for mouse and keyboard handling. Note that there is no render callback; GLFW puts the user in charge, instead of running a rendering loop behind the scenes. The main loop handles UI events and rendering. The simulation is handled in a background thread, which is synchronized with the main thread.

The mouse and keyboard callbacks perform whatever action is necessary. Many of these actions invoke functionality provided by MuJoCo’s abstract visualization mechanism. Indeed this mechanism is designed to be hooked to mouse and keyboard events more or less directly, and provides camera as well as perturbation control.

The profiler and sensor data plots illustrate the use of the mjr_figure function that can plot elaborate 2D figures with grids, annotation, axis scaling etc. The information presented in the profiler is extracted from the diagnostic fields of mjData. It is a very useful tool for tuning the parameters of the constraint solver algorithms. The outputs of the sensors defined in the model are visualized as a bar graph.

Note that the profiler shows timing information collected with high-resolution timers. On Windows, depending on the power settings, the OS may reduce the CPU frequency; this is because sleeps most of the time in order to slow down to realtime. This results in inaccurate timings. To avoid this problem, change the Windows power plan so that the minimum processor state is 100%.


This code sample simulates the passive dynamics of a given model, renders it offscreen, reads the color and depth pixel values, and saves them into a raw data file that can then be converted into a movie file with tools such as ffmpeg. The rendering is simplified compared to because there is no user interaction, visualization options or timing; instead we simply render with the default settings as fast as possible. The dimensions and number of multi-samples for the offscreen buffer are specified in the MuJoCo model, while the simulation duration, frames-per- second to be rendered (usually much less than the physics simulation rate), and output file name are specified as command-line arguments. For example, a 5 second animation at 60 frames per second is created with:

render humanoid.xml 5 60 rgb.out

The default humanoid.xml model specifies offscreen rendering with 800x800 resolution. With this information in hand, we can compress the (large) raw date file into a playable movie file:

ffmpeg -f rawvideo -pixel_format rgb24 -video_size 800x800
  -framerate 60 -i rgb.out -vf "vflip" video.mp4

This sample can be compiled in three ways which differ in how the OpenGL context is created: using GLFW with an invisible window, using OSMesa, or using EGL. The latter two options are only available on Linux and are envoked by defining the symbols MJ_OSMESA or MJ_EGL when compiling The functions initOpenGL and closeOpenGL create and close the OpenGL context in three different ways depending on which of the above symbols is defined.

Note that the MuJoCo rendering code does not depend on how the OpenGL context was created. This is the beauty of OpenGL: it leaves context creation to the platform, and the actual rendering is then standard and works in the same way on all platforms. In retrospect, the decision to leave context creation out of the standard has led to unnecessary proliferation of overlapping technologies, which differ not only between platforms but also within a platform in the case of Linux. The addition of a couple of extra functions (such as those provided by OSMesa for example) could have avoided a lot of confusion. EGL is a newer standard from Khronos which aims to do this, and it is gaining popularity. But we cannot yet assume that all users have it installed.


This code sample illustrates the numerical approximation of forward and inverse dynamics derivatives via finite differences. The process involves a number of epochs. In each epoch the simulation is advanced for a specified number of steps, derivatives are computed at the last state, and timing and accuracy statistics are collected. The averages over epochs are printed at the end.

The code can be incorporated in user projects where derivatives are needed, and can also be used as a stand-alone tool for estimating CPU time and numerical accuracy. Accuracy is estimated in the function checkderiv() using several mathematical identities about the derivatives of inverse functions; the residuals being computed would be zero if the derivatives were exact. Note that these identities involve matrix multiplications which may affect the accuracy estimates. Timing tests are applied only to the parallel section, where the function worker() is executed in multiple threads using OpenMP. There are fewer threads than forward/inverse dynamics evaluations, thus each thread executes multiple evaluations. For a more general discussion of parallel processing in MuJoCo see multi-threading below.

Recall than for a differentiable function f(x) the derivative can be approximated as

df/dx = (f(x+eps)-f(x))/eps

where eps is a small number. One can also use the centered finite difference method, which is two times slower but more accurate. Here f is one of the functions

forward dynamics:  qacc(qfrc_applied, qvel, qpos)
inverse dynamics:  qfrc_inverse(qacc, qvel, qpos)

The code sample computes six Jacobian matrices, containing the derivative of each function with respect to its three arguments. The results are stored in the array deriv. All six Jacobian matrices are square, with dimensionality equal to the number of degrees of freedom mjModel.nv. When the model configuration includes quaternion joints, mjData.qpos has larger dimensionality than the other vectors, however the derivative is only defined in the tangent space to the configuration manifold. This is why, when differentiating with respect to the elements of mjData.qpos, we do not directly add eps but instead use the function mju_quatIntegrate to perturb the quaternion in the tangent space, keeping it normalized. This technique should also be used in any other situation where quaternions need to be perturbed.

There are some important subtleties in this code that improve speed as well as accuracy. To speed up the computation, we re-use intermediate results whenever possible. This relies on the skip mechanism described under forward dynamics and inverse dynamics below. We first perturb force dimensions, keeping position and velocity fixed. In this way we avoid recomputing results that depend on position and velocity but not on force. Then we perturb velocity dimensions, and avoid recomputing results that depend on position but not on velocity or force. Finally we perturb position dimensions - which requires full computation because everything depends on position.

Accuracy depends on the value of eps which is user-adjustable, as well as the shape of the function. In the case of forward dynamics however, the function evaluation involves an iterative constraint solver, and this must be handled with care. In general, the difference between f(x+eps) and f(x) is very small, thus any noise affecting the two function evaluations differently can make the resulting derivatives meaningless. Different warm-starts or different number of solver iterations can act as such noise here. Therefore we fix the warm-start mjData.qacc to a value pre-computed at the center point, using nwarmup extra major iterations to obtain a more accurate warm-start. We also fix the number of solver iterations to niter and set mjModel.opt.tolerance = 0; this disables the early termination mechanism. Note that the original simulation options are restored in the serial code which advances the state.

We emphasize that the above subtleties are not high-order corrections that can be incorporated later. In the presence of unilateral constraints, numerical derivatives are hard to compute and there is no shortcut around it; indeed they would not even be defined if it wasn’t for our soft-constraint model. Making the constraints softer results in more accurate results. This effect is so strong that in some situations it makes sense to intentionally work with the wrong model, i.e., a model that is softer than desired, so as to obtain more accurate derivatives.