A modular approach for kinematic and dynamic modeling of complex robotic systems using algebraic geometry

Shivesh Kumar; Andreas Müller

In: Invited Talk at SIAM AG Conference. SIAM Conference on Applied Algebraic Geometry (SIAM AG-2019), Minisymposium on Algebraic Geometry for Kinematics and Dynamics in Robotics, July 9-13, Bern, Switzerland, SIAM, 7/2019.


Parallel mechanisms are increasingly being used as a modular subsystem units in the design of modern robotic systems for their superior stiffness and payload to weight ration. This leads to series-parallel hybrid robots which combine the advantages of both serial and parallel topologies but also inherit their kinematic complexity. One of the main challenges in modeling and simulation of these complex robotic systems is the existence of kinematic loops. Standard approaches in multi-body kinematics and dynamics adopt numerical resolution of loop closure constraints which leads to accuracy and inefficiency problems. These approaches give you a limited understanding of the geometry of the system. Recently, approaches from computational algebraic geometry have enabled a global description of the kinematic behavior of these complex systems. In this talk, we present a modular and analytical approach towards exploiting these algebraic methods for kinematics and dynamics modeling. This approach forms the basis of a software workbench called Hybrid Robot Dynamics (HyRoDyn). Further, we demonstrate its application in multi-body simulation and control of a complex series-parallel humanoid.


Weitere Links

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence