Efficient Derivative Evaluation for Rigid-Body Dynamics Based on Recursive Algorithms Subject to Kinematic and Loop Constraints

Simulation and control of robotic and bio-mechanical systems depend on a mathematical model description, typically a rigid-body system connected by joints, for which efficient algorithms to compute the forward or inverse dynamics exist. Gradient-based optimization and control methods require derivat...

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Vydané v:IEEE control systems letters Ročník 3; číslo 3; s. 619 - 624
Hlavní autori: Kudruss, Manuel, Manns, Paul, Kirches, Christian
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: IEEE 01.07.2019
Predmet:
control applications
Dynamics
Heuristic algorithms
Kinematics
Libraries
Mathematical model
Numerical algorithms
Optimal control
robotics
Robots
ISSN:2475-1456, 2475-1456
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Popis
Shrnutí:Simulation and control of robotic and bio-mechanical systems depend on a mathematical model description, typically a rigid-body system connected by joints, for which efficient algorithms to compute the forward or inverse dynamics exist. Gradient-based optimization and control methods require derivatives of the dynamics, often approximated by numerical differentiation (FD). However, they benefit from accurate gradients, which promote faster convergence, less iterations, and improved handling of nonlinearities or ill-conditioning of the problem formulations, which are particularly observed when kinematic constraints are involved. In this letter, we apply algorithmic differentiation (AD) to propagate sensitivities through dynamics algorithms. To this end, we augment the computational graph of these algorithms with derivative information. We provide analytic derivatives for elementary operations, in particular matrix factorizations of the descriptor form of the equation of motions, which yields a very efficient derivative evaluation for constrained dynamics. The proposed approach is implemented within the free software package rigid body dynamics library (RBDL), which heavily employs so-called spatial transformations in its implementation of the dynamics algorithms. Thus, manipulations of spatial transformations are treated as elementary operations. The efficiency is improved further by sparsity exploitation. We validate and benchmark the implementation against its FD counterpart for a lifting motion of a human model.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2019.2914338