Linear-time dynamics using Lagrange multipliers
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Robot Dynamics Algorithm
Efficient Factorization of the Joint-Space Inertia Matrix for Branched Kinematic Trees
International Journal of Robotics Research
Rigid Body Dynamics Algorithms
Rigid Body Dynamics Algorithms
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The generalized inertia matrix and its inverse are used extensively in robotics applications. While construction of the inertia matrix requires Θ(n2) time, inverting it traditionally employs algorithms running in time O(n3). We describe an algorithm that reduces the asymptotic time complexity of this operation to the theoretical minimum: Θ(n2). We also present simple modifications that reduce the number of arithmetic operations (and thereby the running time). We compare our approach against fast Cholesky factorization both theoretically (using number of arithmetic operations) and empirically (using running times). We demonstrate our method to dynamically simulate a highly articulated robot undergoing contact, yielding an order of magnitude decrease in running time over existing methods.