Related papers: Exponentially Stable First Order Control on Matrix…
We review matrix methods as applied to tracer transport. Because tracer transport is linear, matrix methods are an ideal fit for the problem. A gridded, Eulerian tracer simulation can be approximated as a system of linear ordinary…
One of the most challenging issues in adaptive control of robot manipulators with kinematic uncertainties is requirement of the inverse of Jacobian matrix in regressor form. This requirement is inevitable in the case of the control of…
Autonomous surface vehicles (ASVs) are influenced by environmental disturbances such as wind and waves, making accurate trajectory tracking a persistent challenge in dynamic marine conditions. In this paper, we propose an efficient…
This paper presents a unified algorithm for motion and force control for a six degree-of-freedom spatial manipulator. The motion-force controller performs trajectory tracking, maneuvering the manipulator's end-effector through desired…
Platooning of autonomous vehicles has the potential to increase safety and fuel efficiency on highways. The goal of platooning is to have each vehicle drive at a specified speed (set by the leader) while maintaining a safe distance from its…
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 $\mathfrak{se}(3)$,…
The scope of this research is a problem of the direct model reference adaptive control of linear time-invariant multi-input multi-output (MIMO) plants without any a priori knowledge about system matrices. To handle it, a new method is…
This paper presents global tracking strategies for the attitude dynamics of a rigid body. It is well known that global attractivity is prohibited for continuous attitude control systems on the special orthogonal group. Such topological…
The objective of this paper is to study the controllability of discrete-time linear control systems in solvable Lie groups. In the special case of nilpotent Lie groups, a necessary and sufficient condition for controllability is…
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…
Accurate tracking of planned trajectories in the presence of perturbations is an important problem in control and robotics. Symmetry is a fundamental mathematical feature of many dynamical systems and exploiting this property offers the…
Consistent localization of cooperative multi-robot systems during navigation presents substantial challenges. This paper proposes a fault-tolerant, multi-modal localization framework for multi-robot systems on matrix Lie groups. We…
This paper presents a hybrid attitude and gyro-bias observer designed directly on the Special Orthogonal group SO(3). The proposed hybrid observer, relying on a hysteresis-based switching between two configurations, guarantees global…
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…
A spherical robot consists of an externally spherical rigid body rolling on a two-dimensional surface, actuated by an auxiliary mechanism. For a class of actuation mechanisms, we derive a controller for the geometric center of the sphere to…
We propose a learning-based trajectory tracking controller for autonomous robotic platforms whose motion can be described kinematically on $\mathrm{SE}(3)$. The controller is formulated in the dual quaternion framework and operates at the…
We present a new class of high-order variational integrators on Lie groups. We show that these integrators are symplectic, momentum preserving, and can be constructed to be of arbitrarily high-order, or can be made to converge…
This paper deals with the design of globally exponentially stable invariant observers on the Special Euclidian group SE(3). First, we propose a generic hybrid observer scheme (depending on a generic potential function) evolving on…
Tracking on the rotation group is a key component of many modern systems for estimation of the motion of rigid bodies. To address this problem, here we describe a Bayesian algorithm that relies on directional measurements for tracking on…
In this paper, we investigate the control sets of linear control systems on the Heisenberg group associated with singular derivations. Under the Lie algebra rank condition, we provide a complete characterization of these sets by analyzing…