Related papers: Log-linear Backstepping control on $SE_2(3)$
Errors dynamics captures the evolution of the state errors between two distinct trajectories, that are governed by the same system rule but initiated or perturbed differently. In particular, state observer error dynamics analysis in matrix…
A dynamic backstepping method is proposed to design controllers for nonlinear systems in the pure-feedback form, for which the traditional backstepping method suffers from solving the implicit nonlinear algebraic equation. The idea of this…
This paper presents a cascaded control architecture, based on nonlinear dynamic inversion (NDI), for rigid body attitude control. The proposed controller works directly with the rotation matrix parameterization, that is, with elements of…
After its introduction, impedance control has been utilized as a primary control scheme for robotic manipulation tasks that involve interaction with unknown environments. While impedance control has been extensively studied, the geometric…
We extend the method of controlled Lagrangians with kinetic shaping to those mechanical systems on semidirect product Lie groups with broken symmetry, more specifically to the Euler--Poincar\'e equations with advected parameters. We find a…
This paper addresses reinforcement learning based, direct signal tracking control with an objective of developing mathematically suitable and practically useful design approaches. Specifically, we aim to provide reliable and easy to…
In this paper we present a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure. We view the nonlinear systems as composed of a finite number of ``pieces,'' which are interpolated by…
This paper presents a constraint-enforcing control framework for a class of discrete-time strict-feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set…
We present here the details of a backstepping transformation aiming at reformulating the dynamics of a nonlinear systems subject to unknown long input delay in a form which is suitable for Lyapunov stability analysis. The control law…
This paper provides new results for a robust adaptive tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid…
Backstepping is a mature and powerful Lyapunov-based design approach for a specific set of systems. Throughout the development over three decades, innovative theories and practices have extended backstepping to stabilization and tracking…
This paper addresses forward motion control for trajectory tracking and mobile formation coordination for a group of non-holonomic vehicles on SE(2). Firstly, by constructing an intermediate attitude variable which involves vehicles'…
This paper studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…
In this paper, the dynamics of nonholonomic systems on Lie groups with a left-invariant kinetic energy and left-invariant constraints are considered. Equations of motion form a closed system of differential equations on the corresponding…
Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This…
Bilinear systems emerge in a wide variety of fields as natural models for dynamical systems ranging from robotics to quantum dots. Analyzing controllability of such systems is of fundamental and practical importance, for example, for the…
Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…
Achieving stable hopping has been a hallmark challenge in the field of dynamic legged locomotion. Controlled hopping is notably difficult due to extended periods of underactuation combined with very short ground phases wherein ground…
The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to…
We provide theoretical guarantees for recursive feasibility and practical exponential stability of the closed-loop system of a feedback linearizable nonlinear system when controlled by a robust data-driven nonlinear predictive control…