Convex Optimisation for Inverse Kinematics

Yenamandra, Tarun; Bernard, Florian; Wang, Jiayi; Mueller, Franziska; Theobalt, Christian

doi:10.1109/3dv.2019.00043

Cited by 11 publications

(3 citation statements)

References 38 publications

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“…Non-linear optimization methods with global convergence properties have been proposed in order to find a minimizer to non-linear optimization problems (NLP) like (1) for some given norm [40], [41]. However, these methods are usually computationally heavy and cannot be applied in real-time control.…”

Section: A Kinematic Controlmentioning

confidence: 99%

The hierarchical Newton's method for numerically stable prioritized dynamic control

Pfeiffer¹,

Escande²,

Gergondet³

et al. 2023

Preprint

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This work links optimization approaches from hierarchical least-squares programming to instantaneous prioritized whole-body robot control. Concretely, we formulate the hierarchical Newton's method which solves prioritized non-linear least-squares problems in a numerically stable fashion even in the presence of kinematic and algorithmic singularities of the approximated kinematic constraints. These results are then transferred to control problems which exhibit the additional variability of time. This is necessary in order to formulate acceleration based controllers and to incorporate the second order dynamics. However, we show that the Newton's method without complicated adaptations is not appropriate in the acceleration domain. We therefore formulate a velocity based controller which exhibits second order proportional derivative convergence characteristics. Our developments are verified in toy robot control scenarios as well as in complex robot experiments which stress the importance of prioritized control and its singularity resolution.

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Section: A Kinematic Controlmentioning

confidence: 99%

The hierarchical Newton's method for numerically stable prioritized dynamic control

Pfeiffer¹,

Escande²,

Gergondet³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Some approaches forgo the joint angle parametrization in favour of Cartesian coordinates and geometric representations [30]. Dai et al [31] use a Cartesian parameterization together with a piecewise-convex relaxation of SO(3) to formulate IK as a mixed-integer linear program, while Yenamandra et al [32] use a similar relaxation to formulate IK as a semidefinite program. Naour et al [33] express IK as a nonlinear program over inter-point distances, showing that solutions can be recovered for unconstrained articulated bodies.…”

Section: Related Workmentioning

confidence: 99%

One Network, Many Robot: Generative Graphical Inverse Kinematics

Limoyo¹,

Marić²,

Giamou³

et al. 2022

Preprint

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Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for robotic manipulation. Existing numerical solvers are broadly applicable, but rely on local search techniques to manage highly nonconvex objective functions. Recently, learning-based approaches have shown promise as a means to generate fast and accurate IK results; learned solvers can easily be integrated with other learning algorithms in end-to-end systems. However, learning-based methods have an Achilles' heel: each robot of interest requires a specialized model which must be trained from scratch. To address this key shortcoming, we investigate a novel distance-geometric robot representation coupled with a graph structure that allows us to leverage the flexibility of graph neural networks (GNNs). We use this approach to train the first learned generative graphical inverse kinematics (GGIK) solver that is, crucially, "robot-agnostic"a single model is able to provide IK solutions for a variety of different robots. Additionally, the generative nature of GGIK allows the solver to produce a large number of diverse solutions in parallel with minimal additional computation time, making it appropriate for applications such as sampling-based motion planning. Finally, GGIK can complement local IK solvers by providing reliable initializations. These advantages, as well as the ability to use task-relevant priors and to continuously improve with new data, suggest that GGIK has the potential to be a key component of flexible, learning-based robotic manipulation systems. † denotes equal contribution.

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“…Their formulation can detect infeasible problems and provide approximate solutions to feasible problems, at the cost of a computationally intensive solution method. Yenamandra et al [34] use a similar relaxation to formulate IK as a semidefinite program. Blanchini et al [35], [4] treat points on a rigid manipulator as virtual masses in a potential field, leading to "minimum energy" solutions to convex formulations of planar and spherical inverse kinematics.…”

Section: A Inverse Kinematicsmentioning

confidence: 99%

Riemannian Optimization for Distance-Geometric Inverse Kinematics

Marić,

Giamou,

Hall

et al. 2021

Preprint

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Solving the inverse kinematics problem is a fundamental challenge in motion planning, control, and calibration for articulated robots. Kinematic models for these robots are typically parameterized by joint angles, generating a complicated mapping between a robot's configuration and end-effector pose. Alternatively, the kinematic model and task constraints can be represented using invariant distances between points attached to the robot. In this paper, we formalize the equivalence of distancebased inverse kinematics and the distance geometry problem for a large class of articulated robots and task constraints. Unlike previous approaches, we use the connection between distance geometry and low-rank matrix completion to find inverse kinematics solutions by completing a partial Euclidean distance matrix through local optimization. Furthermore, we parameterize the space of Euclidean distance matrices with the Riemannian manifold of fixed-rank Gram matrices, allowing us to leverage a variety of mature Riemannian optimization methods. Finally, we show that bound smoothing can be used to generate informed initializations without significant computational overhead, improving convergence. We demonstrate that our novel inverse kinematics solver achieves higher success rates than traditional techniques, and significantly outperforms them on problems that involve many workspace constraints.

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Convex Optimisation for Inverse Kinematics

Cited by 11 publications

References 38 publications

The hierarchical Newton's method for numerically stable prioritized dynamic control

The hierarchical Newton's method for numerically stable prioritized dynamic control

One Network, Many Robot: Generative Graphical Inverse Kinematics

Riemannian Optimization for Distance-Geometric Inverse Kinematics

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