A Propagation Perspective on Recursive Forward Dynamics for Systems With Kinematic Loops

We revisit the concept of constraint embedding as a means for dealing with kinematic loop constraints during dynamics computations for rigid-body systems. Specifically, we consider the local loop constraints emerging from common actuation submechanisms in modern robotics systems (e.g., geared motors...

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Veröffentlicht in:IEEE transactions on robotics Jg. 41; S. 5584 - 5603
Hauptverfasser: Chignoli, Matthew, Adrian, Nicholas, Kim, Sangbae, Wensing, Patrick M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 2025
Schlagworte:
Algebra
Analytical models
Benchmark testing
Dynamics
Force
Heuristic algorithms
humanoid robots
Kinematics
Legged locomotion
legged robots
Mathematical models
recursive algorithms
Robots
Vectors
ISSN:1552-3098, 1941-0468
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Zusammenfassung:We revisit the concept of constraint embedding as a means for dealing with kinematic loop constraints during dynamics computations for rigid-body systems. Specifically, we consider the local loop constraints emerging from common actuation submechanisms in modern robotics systems (e.g., geared motors, differential drives, and four-bar mechanisms). As a complementary perspective to prior work on constraint embedding, we present an analysis that generalizes the traditional concepts of joint models and motion/force subspaces between individual rigid bodies to generalized joint models and motion/force subspaces between groups of rigid bodies subject to loop constraints. We then use these generalized concepts to derive the constraint-embedded recursive forward dynamics algorithm using multihandle articulated bodies. We demonstrate the broad applicability of the generalized joint concepts by showing how they also lead to the constraint-embedding-based recursive algorithm for inverse dynamics. Lastly, we benchmark our open-source implementation in C++ for the forward dynamics algorithm against state-of-the-art, sparsity-exploiting algorithms. Our alternative derivation is intended to make the constraint-embedding methodology more accessible to the broader robotics community, while the benchmarking study clarifies the relative strengths and limitations of constraint embedding versus sparsity-exploiting methods. Indeed, our benchmarking validates that constraint embedding outperforms the nonrecursive alternative in cases involving local kinematic loops.
ISSN:1552-3098
1941-0468
DOI:10.1109/TRO.2025.3593081