Related papers: Manipulator Differential Kinematics: Part 2: Accel…
In this paper, we propose to estimate the forward dynamics equations of mechanical systems by learning a model of the inverse dynamics and estimating individual dynamics components from it. We revisit the classical formulation of rigid body…
Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely…
We present a theoretical and numerical analysis of the kinematics for the "Transpressor", a cuspidal 6R robot. It admits up to 16 inverse kinematics solutions which are described geometrically. For special target poses, we provide the…
The kinematics of a robot manipulator are described in terms of the mapping connecting its joint space and the 6-dimensional Euclidean group of motions $SE(3)$. The associated Jacobian matrices map into its Lie algebra $\mathfrak{se}(3)$,…
Solving the analytical inverse kinematics (IK) of redundant manipulators in real time is a difficult problem in robotics since its solution for a given target pose is not unique. Moreover, choosing the optimal IK solution with respect to…
The Newton, Gauss--Newton and Levenberg--Marquardt methods all use the first derivative of a vector function (the Jacobian) to minimise its sum of squares. When the Jacobian matrix is ill-conditioned, the function varies much faster in some…
In this paper, we propose a class of general second-order primal-dual dynamical systems with Tikhonov regularization and Hessian-driven damping for solving convex-concave bilinear saddle point problems. The proposed dynamical system…
In a multi-agent network, we consider the problem of minimizing an objective function that is expressed as the sum of private convex and smooth functions, and a (possibly) non-differentiable convex regularizer. We propose a novel…
In this work, a novel Dynamic Movement Primitive (DMP) formulation is proposed which supports reversibility, i.e. backwards reproduction of a learned trajectory. Apart from sharing all favourable properties of the original DMP, decoupling…
Quasi-Newton methods form an important class of methods for solving nonlinear optimization problems. In such methods, first order information is used to approximate the second derivative. The aim is to mimic the fast convergence that can be…
We present a novel method for learning hybrid force/position control from demonstration. We learn a dynamic constraint frame aligned to the direction of desired force using Cartesian Dynamic Movement Primitives. In contrast to approaches…
Daily manipulation tasks are characterized by geometric primitives related to actions and object shapes. Such geometric descriptors are poorly represented by only using Cartesian coordinate systems. In this paper, we propose a learning…
The Hessian-vector product has been utilized to find a second-order stationary solution with strong complexity guarantee (e.g., almost linear time complexity in the problem's dimensionality). In this paper, we propose to further reduce the…
The majority of inverse kinematics (IK) algorithms search for solutions in a configuration space defined by joint angles. However, the kinematics of many robots can also be described in terms of distances between rigidly-attached points,…
Robotic systems are often complex and depend on the integration of a large number of software components. One important component in robotic systems provides the calculation of forward kinematics, which is required by both motion-planning…
This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…
Traditional offline redundancy resolution of trajectories for redundant manipulators involves computing inverse kinematic solutions for Cartesian space paths, constraining the manipulator to a fixed path without real-time adjustments.…
Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with…
We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins, Kress and Miller (2010). This expansion method expresses the integral in a finite power series in terms of lower…
In Part V of this study, we presented an original Lagrangian approach for computing the dynamic characteristics along stationary rays, by solving the linear, second-order Jacobi differential equation, considering four sets of initial…