# Linearization of manipulator dynamics using spatial operators

@article{Jain1993LinearizationOM, title={Linearization of manipulator dynamics using spatial operators}, author={Abhinandan Jain and Guillermo Rodr{\'i}guez}, journal={IEEE Trans. Syst. Man Cybern.}, year={1993}, volume={23}, pages={239-248} }

Techniques from the spatial operator algebra are used to obtain closed-form operator expressions for two types of linearized dynamics models: the linearized inverse and forward dynamics models. Spatially recursive algorithms of O(n) and O(n/sup 2/) complexity for the computation of the perturbation vector and coefficient matrices for the linearized inverse dynamics model (LIDM) are developed. Operator factorization and inversion identities are used to develop corresponding closed-form…

## 33 Citations

### Efficient Analytical Derivatives of Rigid-Body Dynamics Using Spatial Vector Algebra

- Computer ScienceIEEE Robotics and Automation Letters
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This letter provides closed-form spatial-vector expressions for the first-order partial derivatives of inverse dynamics, and a highly efficient recursive algorithm based on these expressions, which is applicable for robots with general multi-DoF Lie group joints (e.g., revolute, spherical, and floating base).

### Closed-Form Second-Order Partial Derivatives of Rigid-Body Inverse Dynamics

- MathematicsArXiv
- 2022

Optimization-based control methods for robots often rely on first-order dynamics approximation methods like in iLQR. Using second-order approximations of the dynamics is expensive due to the costly…

### Analytical Second-Order Partial Derivatives of Rigid-Body Inverse Dynamics

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— Optimization-based robot control strategies often rely on ﬁrst-order dynamics approximation methods, as in iLQR. Using second-order approximations of the dynamics is expensive due to the costly…

### Symbolic computation of the inverse dynamics of elastic joint robots

- EngineeringIEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004
- 2004

This paper presents a method for recursive calculation of the inverse dynamics of real-world robots considering elasticity and gyroscopic effects introduced by the drivetrains by means of higher-order time derivatives of spatial operators proposed by the spatial operator algebra.

### Recursive Algorithms Using Local Constraint Embedding for Multibody System Dynamics

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- 2009

This paper describes a constraint embedding approach for handling of local closure constraints in multibody system dynamics. The approach uses spatial operator techniques to eliminate local-loop…

### Accelerating Second-Order Differential Dynamic Programming for Rigid-Body Systems

- Computer ScienceIEEE Robotics and Automation Letters
- 2021

This letter presents a method to reduce the computational demands of including second-order dynamics sensitivity information into the Differential Dynamic Programming (DDP) trajectory optimization…

### Tensor-Free Second-Order Differential Dynamic Programming

- Computer ScienceArXiv
- 2021

A tensor-free approach to DDP is developed where all the necessary derivatives are computed with the same complexity as in the iterative Linear Quadratic Regulator (iLQR).

### Computing Inter-Body Constraint Forces in Recursive Multibody Dynamics

- Computer Science
- 2018

This paper shows that there are simple and very low cost methods available to compute the constraint forces that directly use articulated body algorithm quantities that are by products of the recursive solution process.

### Multibody Mass Matrix Sensitivity Analysis Using Spatial Operators

- Engineering, Mathematics
- 2003

This paper focuses on the computation of the sensitivity of the system mass matrix for tree-topology multibody systems and develops an analytical expression for the same using spatial operators.

### Using the algebraic structure of articulated robot dynamics in control design

- MathematicsProceedings of the 36th IEEE Conference on Decision and Control
- 1997

We discuss the algebraic structure of the dynamics of articulated multibody systems and how it may be effectively used in control design. The dynamics has a decomposition consisting of matrix…

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