Hybrid Robot Dynamics

Hybrid Robot Dynamics (HyRoDyn) is an analytical and modular software workbench written in C++ for solving kinematics and dynamics of highly complex series-parallel hybrid robots which are becoming increasingly popular in the recent years. They inherit advantages and kinematic complexity of both architectures and hence require careful treatment in their analysis and control. Instead of resorting to numerical resolution of loop closure constraints, this software workbench provides a holistic approach towards dealing with the complexity of these systems by re-utilizing the closed form solution to loop closure constraints of parallel mechanisms commonly used in the design of series-parallel hybrid robots. Kinematicians are welcome to contribute to the submechanism libraries in HyRoDyn so that catalog of supported parallel mechanisms can be enriched. This software tool serves as an efficient and error-free alternative to the already existing generic numerical multi-body kinematics and dynamics software.
Keywords: series-parallel hybrid robots
Status: active
Operating system: Linux
Programming languages: C++, Python, Ruby
Ownership: This software was developed by the DFKI as well as by the Robotics Research Group and the University of Bremen and is being further developed under this responsibility. For questions and suggestions, please refer to the contact persons.

Software description

Example of series-parallel hybrid composition
Vertical movement of humanoid leg

Parallel mechanisms are increasingly being used as modular subsystem units in various robots and man-machine interfaces for their superior stiffness, payload-to-weight ratio and dynamic properties. This leads to series-parallel hybrid robotic systems which are difficult to model and control due to the presence of various closed loops. Most model- based kinematic and dynamic modeling tools resolve loop closure constraints numerically and hence may suffer from inefficiency and accuracy issues. Also, they do not exploit the modularity in robot design. Further, such systems can have variable mobility, different assembly modes and can impose redundant constraints on the equations of motion.  Hence, it is interesting for kinematics researchers to study the analytical solutions to geometric problems associated with a specific type of PM and their importance over numerical solutions is irrefutable.  But this domain-specific knowledge is often underrepresented in the design of model-based kinematics and dynamics software frameworks.

Hybrid Robot Dynamics (HyRoDyn) is an analytical and modular software workbench written in C++ for solving kinematics and dynamics of highly complex series-parallel hybrid robots. The main idea behind HyRoDyn is to store the closed form solutions to the loop closure constraints in a configurable mechanism library which is identified by its type (for e.g. 1-RRPR, 2SPU+1U, 2SPRR+1U, 6-UPS).  Based on submechanisms defined in a hybrid robot, HyRoDyn can modularly compose the loop closure function of the overall system in an automated way. The resulting loop closure Jacobian has a block diagonal structure that can be exploited in the computation of various forward and inverse kinematics and dynamics algorithms. HyRoDyn is implemented in C++ and utilizes recursive O(n) multi-body dynamics  algorithms  for  tree  type  systems  from  the Rigid Body Dynamics Library (RBDL) based on Featherstone's algorithms. Presently, closed form solutions to mechanisms such as 1-RRPR, 2-SPU+1U, 2-SPRR+1U, 6-RUS, 6-UPS, parallelogram chains are available in its submechanism libraries and HyRoDyn can be used to analytically solve the kinematics and dynamics of arbitrary series-parallel hybrid robots composed of these submechanism modules. Actuation of the robot can be arbitrarily selected.

The input to HyRoDyn is SMURF file which can be generated using a Blender-based visual editor called Phobos. The use of visual editor makes it easy to annotate the parallel submechanism modules in a robot and assemble them to build highly complex robot models. Further, HyRoDyn has been integrated in the Robot Construction Kit (RoCK) middleware as an orogen component which provide both forward and inverse mappings between independent joint space of the robot and its actuation space at position, velocity, acceleration and force levels. The HyRoDyn-orogen component can be used for simulation as well as real time control of complex series-parallel hybrid robotic systems.


Application Field: Space Robotics
Logistics, Production and Consumer
Assistance- and Rehabilitation Systems
Related Projects: TransFIT
Flexible Interaction for infrastructures establishment by means of teleoperation and direct collaboration; transfer into industry 4.0 (07.2017- 12.2021)
Learning and Verifying Complex Behaviours for Humanoid Robots (06.2020- 05.2024)
Human-Machine Interaction Modeling for Continuous Improvement of Robot Behavior (08.2021- 07.2024)
Feasibility study for simulated micro gravity based on an exoskeleton: No Gravity Exoskeleton (NoGravEx) (01.2022- 12.2023)
Recupera REHA
Full-body exoskeleton for upper body robotic assistance (09.2014- 12.2017)
Models, methods and tools for the model based software development of robots (06.2015- 05.2018)
AI-based Qualification of Deliberative Behaviour for a Robotic Construction Kit (08.2018- 07.2021)
Related Robots: Full Body Exoskeleton
Exoskeleton for upper body robotic assistance
Dual Arm Exoskeleton
Exoskeleton for upper body robotic assistance (Recupera REHA)
Humanoid robot as an assistance system in a human-optimized environment
RH5 Manus
Humanoid robot as an assistance system in a human-optimized environment
Sponsor: Federal Ministry of Education and Research
German Aerospace Center e.V.
Grant number: Recupera-Reha: 01-IM-14006A D-RoCK: 01IW15001 Q-RoCK: FKZ 01IW18003


D-Rock: HyRoDyn Phobos XEC

Workflow vom Modellieren über das Simulieren bis zur Echtzeitkontrolle bei einer seriell-parallelen Hybridkomposition eines menschenähnlichen Beins.

D-Rock: HyRoDyn - Inverse Dynamik basierend auf einer unabhängigen Gelenkraumbewegung


1. An Analytical and Modular Software Workbench for Solving Kinematics and Dynamics of Series-Parallel Hybrid Robots
Shivesh Kumar, Andreas Mueller
In 43rd Mechanisms and Robotics Conference, Parts A and B, (IDETC/CIE-2019), 18.8.-21.8.2019, Anaheim, CA, ASME, Oct/2019.

2. HyRoDyn: A Modular Software Framework for Solving Analytical Kinematics and Dynamics of Series-Parallel Hybrid Robots
Shivesh Kumar, Kai Alexander von Szadkowski, Andreas Müller, Frank Kirchner
In Poster at 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems, (IROS-2018), 01.10.-05.10.2018, Madrid, IEEE/RSJ, series IROS Poster proceedings, pages 1-1, Oct/2018.

last updated 21.10.2019
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