Related papers: Quaternion Sliding Variables in Manipulator Contro…
More than 150 years after their invention by Hamilton, quaternions are now widely used in the aerospace and computer animation industries to track the paths of moving objects undergoing three-axis rotations. It is shown here that they…
This paper presents two novel control methodologies for the cooperative manipulation of an object by N robotic agents. Firstly, we design an adaptive control protocol which employs quaternion feedback for the object orientation to avoid…
This paper presents a novel Representation-Free Model Predictive Control (RF-MPC) framework for controlling various dynamic motions of a quadrupedal robot in three dimensional (3D) space. Our formulation directly represents the rotational…
This paper addresses the problem of end-effector formation control for a mixed group of two-link manipulators moving in a horizontal plane that comprises of fully-actuated manipulators and underactuated manipulators with only the second…
This paper addresses the closed-loop control of an actuator with both a continuous input variable (motor torque) and a discrete input variable (mode selection). In many applications, robots have to bear large loads while moving slowly and…
We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how…
We present a model-predictive control (MPC) framework for legged robots that avoids the singularities associated with common three-parameter attitude representations like Euler angles during large-angle rotations. Our method parameterizes…
We introduce motions as real six-dimensional vectors. A motion means a rotation and a translation. We define a motion operator which maps unit dual quaternions to motions, and a UDQ operator which maps motions to unit dual quaternions. By…
Compared to conventional robots, flexible manipulators offer many advantages, such as faster end-effector velocities and less energy consumption. However, their flexible structure can lead to undesired oscillations. Therefore, the applied…
Linear Parameter Varying Dynamical Systems (LPV-DS) encode trajectories into an autonomous first-order DS that enables reactive responses to perturbations, while ensuring globally asymptotic stability at the target. However, the current…
In this paper, we propose and demonstrate an adaptive-sliding mode control for trajectory tracking control of robot manipulators subjected to uncertain dynamics, vibration disturbance, and payload variation disturbance. Throughout this work…
Control of robot orientation in Cartesian space implicates some difficulties, because the rotation group SO(3) is not contractible, and only globally contractible state spaces support continuous and globally asymptotically stable feedback…
The precise motion control of a multi-degree of freedom~(DOF) robot manipulator is always challenging due to its nonlinear dynamics, disturbances, and uncertainties. Because most manipulators are controlled by digital signals, a novel…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
This article is an exhaustive revision of concepts and formulas related to quaternions and rotations in 3D space, and their proper use in estimation engines such as the error-state Kalman filter. The paper includes an in-depth study of the…
We present an orientation adaptive controller to compensate for the effects of highly constrained environments on continuum manipulator actuation. A transformation matrix updated using optimal estimation techniques from optical flow…
This work proposes a control law for a manipulator with the aim of realizing desired time-varying motion-force profiles in the presence of a stiff environment. In many cases, the interaction with the environment affects only one degree of…
Terminal sliding mode (TSM) control algorithm and its non-singular refinement have been elaborated for two decades and belong, since then, to a broader class of the finite-time controllers, which are known to be robust against the matched…
Accurate and robust positioning of rotor axle is essential for efficient and safe operation of high-speed rotational machines with active magnetic bearings. This study presents a cascaded nonlinear control strategy for vertical axial…