3 research outputs found
Convex Optimisation for Inverse Kinematics
We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is a joint that has an associated geometric transformation that is propagated to all its child nodes. The IK problem has various applications in vision and graphics, for example for tracking or reconstructing articulated objects, such as human hands or bodies. Most commonly, the IK problem is tackled using local optimisation methods. A major downside of these approaches is that, due to the non-convex nature of the problem, such methods are prone to converge to unwanted local optima and therefore require a good initialisation. In this paper we propose a convex optimisation approach for the IK problem based on semidefinite programming, which admits a polynomial-time algorithm that globally solves (a relaxation of) the IK problem. Experimentally, we demonstrate that the proposed method significantly outperforms local optimisation methods using different real-world skeletons
Riemannian Optimization for Distance-Geometric Inverse Kinematics
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 parametrized by joint angles, generating a
complicated mapping between the robot configuration and the 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 distance-based 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 parametrize 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 inverse
kinematics solver achieves higher success rates than traditional techniques,
and substantially outperforms them on problems that involve many workspace
constraints.Comment: 20 pages, 14 figure
Convex Optimisation for Inverse Kinematics
We consider the problem of inverse kinematics (IK), where one wants to find
the parameters of a given kinematic skeleton that best explain a set of
observed 3D joint locations. The kinematic skeleton has a tree structure, where
each node is a joint that has an associated geometric transformation that is
propagated to all its child nodes. The IK problem has various applications in
vision and graphics, for example for tracking or reconstructing articulated
objects, such as human hands or bodies. Most commonly, the IK problem is
tackled using local optimisation methods. A major downside of these approaches
is that, due to the non-convex nature of the problem, such methods are prone to
converge to unwanted local optima and therefore require a good initialisation.
In this paper we propose a convex optimisation approach for the IK problem
based on semidefinite programming, which admits a polynomial-time algorithm
that globally solves (a relaxation of) the IK problem. Experimentally, we
demonstrate that the proposed method significantly outperforms local
optimisation methods using different real-world skeletons