Related papers: Model Predictive Tracking Control for Invariant Sy…
Attitude tracking on the unit sphere of dimension $3$ based on sliding mode is considered in this paper. The tangent bundle of Lagrangian dynamics that describes the rotational motion of a rigid body is first shown to be a Lie group, and…
We develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed…
This paper reports on a new error-state Model Predictive Control (MPC) approach to connected matrix Lie groups for robot control. The linearized tracking error dynamics and the linearized equations of motion are derived in the Lie algebra.…
This paper presents a method for local motion planning in unstructured environments with static and moving obstacles, such as humans. Given a reference path and speed, our optimization-based receding-horizon approach computes a local…
This paper presents nonlinear tracking control systems for a quadrotor unmanned aerial vehicle under the influence of uncertainties. Assuming that there exist unstructured disturbances in the translational dynamics and the attitude…
Mechanical control systems such as aerial, marine, space, and terrestrial robots often naturally admit a state-space that has the structure of a Lie group. The kinetic energy of such systems is commonly invariant to the induced action by…
This paper proposes a model predictive trajectory tracking approach for quadrotors subject to input constraints. Our proposed approach relies on a hierarchical control strategy with an outer-loop feedback generating the required thrust and…
We propose a data-driven tracking model predictive control (MPC) scheme to control unknown discrete-time linear time-invariant systems. The scheme uses a purely data-driven system parametrization to predict future trajectories based on…
Differentially flat models are frequently used to design feedforward controllers for electromechanical systems. However, control performance depends on model accuracy, which makes feedback imperative. This paper presents a control scheme…
This paper addresses the motion control problem for underactuated mechanical systems with full attitude control and one translational force input to manage the six degrees of freedom involved in the three-dimensional Euclidean space. These…
This paper presents an adaptive tracking model predictive control (MPC) scheme to control unknown nonlinear systems based on an adaptively estimated linear model. The model is determined based on linear system identification using a moving…
In this paper, we present a learning-based tracking controller based on Gaussian processes (GP) for collision avoidance of multi-agent systems where the agents evolve in the special Euclidean group in the space SE(3). In particular, we use…
We propose a globally exponentially convergent observer for the dynamical system evolving on matrix Lie groups with bounded velocity with unknown bound. We design the observer in the ambient Euclidean space and show exponential convergence…
This paper proposes a Model Predictive Control (MPC) algorithm for target tracking amongst static and dynamic obstacles. Our main contribution lies in improving the computational tractability and reliability of the underlying non-convex…
This paper proposes a framework for adaptively learning a feedback linearization-based tracking controller for an unknown system using discrete-time model-free policy-gradient parameter update rules. The primary advantage of the scheme over…
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…
We develop a model predictive control (MPC) design for systems with discrete-time dynamics evolving on smooth manifolds. We show that the properties of conventional MPC for dynamics evolving on $\mathbb R^n$ are preserved and we develop a…
This work proposes a quaternion-based sliding variable that describes exponentially convergent error dynamics for any forward complete desired attitude trajectory. The proposed sliding variable directly operates on the non-Euclidean space…
We give an exposition of the theory of invariant manifolds around a fixed point, in the case of time-discrete, analytic dynamical systems over a complete ultrametric field K. Typically, we consider an analytic manifold M modelled on an…
The trajectory tracking problem is a fundamental control task in the study of mechanical systems. A key construction in tracking control is the error or difference between an actual and desired trajectory. This construction also lies at the…