Direct methods for sparse matrices
Direct methods for sparse matrices
Dynamic simulation of n-axis serial robotic manipulators using a natural orthogonal complement
International Journal of Robotics Research
Alternate formulations for the manipulator inertia matrix
International Journal of Robotics Research
A spatial operator algebra for manipulator modeling and control
International Journal of Robotics Research
Linear-time dynamics using Lagrange multipliers
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Modeling, Identification and Control of Robots
Modeling, Identification and Control of Robots
Robot Dynamics Algorithm
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Comparative Study on Serial and Parallel Forward Dynamics Algorithms for Kinematic Chains*
International Journal of Robotics Research
Exploiting Sparsity in Operational-space Dynamics
International Journal of Robotics Research
SIMPAR'12 Proceedings of the Third international conference on Simulation, Modeling, and Programming for Autonomous Robots
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This paper describes new factorization algorithms that exploit branch-induced sparsity in the joint-space inertia matrix (JSIM) of a kinematic tree. It also presents new formulae that show how the cost of calculating and factorizing the JSIM vary with the topology of the tree. These formulae show that the cost of calculating forward dynamics for a branched tree can be considerably less than the cost for an unbranched tree of the same size. Branches can also reduce complexity; some examples are presented of kinematic trees for which the complexity of calculating and factorizing the JSIM are less than O(n2) and O(n3) , respectively. Finally, a cost comparison is made between an O(n) algorithm and an O(n3) algorithm, the latter incorporating one of the new factorization algorithms. It is shown that the O(n3) algorithm is only 15% slower than the O(n) algorithm when applied to a 30-degrees-of-freedom humanoid, but is 2.6 times slower when applied to an equivalent unbranched chain. This is due mainly to the O(n3) algorithm running about 2.2 times faster on the humanoid than on the chain.