Equivalence of the Projected Forward Dynamics and the Dynamically Consistent Inverse Solution

João Moura, Vladimir Ivan, Mustapha Suphi Erden, Sethu Vijayakumar

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The analysis, design, and motion planning of robotic systems, often relies on its forward and inverse dynamic models. When executing a task involving interaction with the environment, both the task and the environment impose constraints on the robot’s motion. For modeling such systems, we need to incorporate these constraints in the robot’s dynamic model. In this paper, we define the class of Task-based Constraints (TbC) to prove that the forward dynamic models of a constrained system obtained through the Projection-based Dynamics (PbD), and the Operational Space Formulation (OSF) are equivalent. In order to establish such equivalence, we first generalize the OSF to a rank deficient Jacobian. This generalization allow us to numerically handle redundant constraints and singular configurations, without having to use different controllers in the vicinity of such configurations. We then reformulate the PbD constraint inertia matrix, generalizing all its previous distinct algebraic variations. We also analyse the condition number of different constraint inertia matrices, which affects the numerical stability of its inversion. Furthermore, we show that we can recover the operational space control with constraints from a multiple Task-based Constraint abstraction.
Original languageEnglish
Title of host publicationProceedings of Robotics: Science and Systems
EditorsAntonio Bicchi, Hadas Kress-Gazit, Seth Hutchinson
Place of PublicationFreiburg im Breisgau, Germany
Number of pages10
ISBN (Electronic)978-0-9923747-5-4
Publication statusE-pub ahead of print - 26 Jun 2019
EventRobotics: Science and Systems 2019 - Freiburg im Breisgau, Germany
Duration: 22 Jun 201926 Jun 2019

Publication series

NameRobotics: Science and Systems Proceedings
ISSN (Electronic)2330-765X


ConferenceRobotics: Science and Systems 2019
Abbreviated titleRSS 2019
CityFreiburg im Breisgau
Internet address


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