Ruckig 0.15.0
Motion Generation for Robots and Machines
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Ruckig generates trajectories on-the-fly, allowing robots and machines to react instantaneously to sensor input. Ruckig calculates a trajectory to a target waypoint (with position, velocity, and acceleration) starting from any initial state limited by velocity, acceleration, and jerk constraints. Besides the target state, Ruckig allows to define intermediate positions for waypoint following. For state-to-state motions, Ruckig guarantees a time-optimal solution. With intermediate waypoints, Ruckig calculates the path and its time parametrization jointly, resulting in significantly faster trajectories compared to traditional methods.
More information can be found at ruckig.com and in the corresponding paper Jerk-limited Real-time Trajectory Generation with Arbitrary Target States, accepted for the Robotics: Science and Systems (RSS), 2021 conference.
Ruckig has no dependencies (except for testing). To build Ruckig using CMake, just run
To install Ruckig in a system-wide directory, you can either use (sudo) make install
or install it as debian package using cpack by running
An example of using Ruckig in your CMake project is given by examples/CMakeLists.txt
. However, you can also include Ruckig as a directory within your project and call add_subdirectory(ruckig)
in your parent CMakeLists.txt
.
Ruckig is also available as a Python module, in particular for development or debugging purposes. The Ruckig Community Version can be installed from PyPI via
When using CMake, the Python module can be built using the BUILD_PYTHON_MODULE
flag. If you're only interested in the Python module (and not in the C++ library), you can build and install Ruckig via pip install .
.
Furthermore, we will explain the basics to get started with online generated trajectories within your application. There is also a collection of examples that guide you through the most important features of Ruckig. A time-optimal trajectory for a single degree of freedom is shown in the figure below. We also added plots of the resulting trajectories for all examples. Let's get started!
Ruckig provides three main interface classes: the Ruckig, the InputParameter, and the OutputParameter class.
First, you'll need to create a Ruckig instance with the number of DoFs as a template parameter, and the control cycle (e.g. in seconds) in the constructor.
The input type has 3 blocks of data: the current state, the target state and the corresponding kinematic limits.
If you only want to have a acceleration-constrained trajectory, you can also omit the max_jerk
as well as the current
and target_acceleration
value. Given all input and output resources, we can iterate over the trajectory at each discrete time step. For most applications, this loop must run within a real-time thread and controls the actual hardware.
Within the control loop, you need to update the current state of the input parameter according to the calculated trajectory. Therefore, the pass_to_input
method copies the new kinematic state of the output to the current kinematic state of the input parameter. If (in the next step) the current state is not the expected, pre-calculated trajectory, Ruckig will calculate a new trajectory based on the novel input. When the trajectory has reached the target state, the update
function will return Result::Finished
.
The Ruckig Community Version now supports intermediate waypoints via a cloud API. To allocate the necessary memory for a variable number of waypoints beforehand, we need to pass the maximum number of waypoints to Ruckig via
The InputParameter
class takes the number of waypoints as an optional input, however usually you will fill in the values (and therefore reserve its memory) yourself. Then you're ready to set intermediate via points by
As soon as at least one intermediate positions is given, the Ruckig Community Version switches to the mentioned (of course, non real-time capable) cloud API. If you require real-time calculation on your own hardware, please contact us for the Ruckig Pro Version.
When using intermediate positions, both the underlying motion planning problem as well as its calculation changes significantly. In particular, there are some fundamental limitations for jerk-limited online trajectory generation regarding the usage of waypoints. Please find more information about these limitations here, and in general we recommend to use
to filter waypoints according to a (high) threshold distance. Setting interrupt_calculation_duration makes sure to be real-time capable by refining the solution in the next control invocation. Note that this is a soft interruption of the calculation. Currently, no minimum or discrete durations are supported when using intermediate positions.
To go into more detail, the InputParameter type has following members:
On top of the current state, target state, and constraints, Ruckig allows for a few more advanced settings:
per_section_max_velocity
.We refer to the API documentation of the enumerations within the ruckig
namespace for all available options.
To check that Ruckig is able to generate a trajectory before the actual calculation step,
throws an error with a detailed reason if an input is not valid. You can also set the default template parameter to false via ruckig.validate_input<false>(...)
to just return a boolean true or false. The two boolean arguments check that the current or target state are within the limits. The check includes a typical catch of jerk-limited trajectory generation: When the current state is at maximal velocity, any positive acceleration will inevitable lead to a velocity violation at a future timestep. In general, this condition is fulfilled when
If both arguments are set to true, the calculated trajectory is guaranteed to be within the kinematic limits throughout its duration. Also, note that there are range constraints of the input due to numerical reasons, see below for more details.
The update
function of the Ruckig class returns a Result type that indicates the current state of the algorithm. This can either be working, finished if the trajectory has finished, or an error type if something went wrong during calculation. The result type can be compared as a standard integer.
State | Error Code |
---|---|
Working | 0 |
Finished | 1 |
Error | -1 |
ErrorInvalidInput | -100 |
ErrorTrajectoryDuration | -101 |
ErrorPositionalLimits | -102 |
ErrorExecutionTimeCalculation | -110 |
ErrorSynchronizationCalculation | -111 |
The output class includes the new kinematic state and the overall trajectory.
Moreover, the trajectory class has a range of useful parameters and methods.
Again, we refer to the API documentation for the exact signatures.
Ruckig also supports an offline approach for calculating a trajectory:
When only using this method, the Ruckig
constructor does not need a control cycle (delta_time
) as an argument. However if given, Ruckig supports stepping through the trajectory with
starting from the current output.time
(currently Ruckig Pro only).
When following an arbitrary signal with position, velocity, acceleration, and jerk-limitation, the straight forward way would be to pass the current state to Ruckig's target state. However, as the resulting trajectory will take time to catch up, this approach will always lag behind the signal. The tracking interface solves this problem by predicting ahead (e.g. with constant acceleration by default) and is therefore able to follow signals very closely in a time-optimal way. This might be very helpful for (general) tracking, robot servoing, or trajectory post-processing applications.
To use the tracking interface, construct
and set the current state as well as the kinematic constraints via
Then, we can track a signal in an online manner within the real-time control loop
The Trackig interface has two different modes: One optimized for higher quality tracking and one for faster computation time:
Please find a complete example here. This functionality can also be used in an offline manner, e.g. when the entire signal is known beforehand. Here, we call the
method with the trajectory given as a std::vector
of target states. The Tracking interface is available in the Ruckig Pro version.
So far, we have told Ruckig the number of DoFs as a template parameter. If you don't know the number of DoFs at compile-time, you can set the template parameter to ruckig::DynamicDOFs
and pass the DoFs to the constructor:
This switches the default Vector from the std::array
to the dynamic std::vector
type. However, we recommend to keep the template parameter when possible: First, it has a performance benefit of a few percent. Second, it is convenient for real-time programming due to its easier handling of memory allocations. When using dynamic degrees of freedom, make sure to allocate the memory of all vectors beforehand.
Ruckig supports custom vector types to make interfacing with your code even easier and more flexible. Most importantly, you can switch to Eigen Vectors simply by including Eigen (3.4 or later) before Ruckig
and then call the constructors with the ruckig::EigenVector
parameter.
Now every in- and output of Ruckig's API (such as current_position
, new_position
or max_jerk
) are Eigen types! To define completely custom vector types, you can pass a C++ template template parameter to the constructor. This template template parameter needs to fulfill a range of template arguments and methods:
Note that DynamicDOFs
corresponds to DOFs = 0
. We've included a range of examples for using Ruckig with (10) Eigen, (11) custom vector types, and (12) custom types with a dynamic number of DoFs.
The current test suite validates over 5.000.000.000 random trajectories as well as many additional edge cases. The numerical exactness is tested for the final position and final velocity to be within 1e-8
, for the final acceleration to be within 1e-10
, and for the velocity, acceleration and jerk limit to be within of a numerical error of 1e-12
. These are absolute values - we suggest to scale your input so that these correspond to your required precision of the system. For example, for most real-world systems we suggest to use input values in [m]
(instead of e.g. [mm]
), as 1e-8m
is sufficient precise for practical trajectory generation. Furthermore, all kinematic limits should be below 1e9
. The maximal supported trajectory duration is 7e3
. Note that Ruckig will also output values outside of this range, there is however no guarantee for correctness.
The Ruckig Pro version has additional tools to increase the numerical range and improve reliability. For example, theposition_scale
and time_scale
parameter of the Calculator
class change the internal representation of the input parameters.
This way, you can easily achieve the requirements above even for very high jerk limits or very long trajectories. Note that the scale parameters don't effect the resulting trajectory - they are for internal calculation only.
We find that Ruckig is more than twice as fast as Reflexxes Type IV for state-to-state motions and well-suited for control cycles as low as 250 microseconds. The Ruckig Community Version is in general a more powerful and open-source alternative to the Reflexxes Type IV library. In fact, Ruckig is the first Type V trajectory generator for arbitrary target states and even supports directional velocity and acceleration limits, while also being faster on top.
For trajectories with intermediate waypoints, we compare Ruckig to Toppra, a state-of-the-art library for robotic motion planning. Ruckig is able to improve the trajectory duration on average by around 10%, as the path planning and time parametrization are calculated jointly. Moreover, Ruckig is real-time capable and supports jerk-constraints.
Ruckig is written in C++17. It is continuously tested on ubuntu-latest
, macos-latest
, and windows-latest
against following versions
A C++11 and C++03 version of Ruckig is also available - please contact us if you're interested.
Ruckig is used by over hundred research labs, companies, and open-source projects worldwide, including: