Nonlinear Model Predictive Control for Constrained Output Path Following

We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following problems. Specifically, we propose a predictive control approach to constrained path-following problems with and without velocity assignments and provide sufficient convergence conditions based on terminal regions and end penalties. Furthermore, we analyze the geometric nature of constrained output path-following problems and thereby provide insight into the computation of suitable terminal control laws and terminal regions. We draw upon an example from robotics to illustrate our findings.Comment: 12 pages, 4 figure

Perception-aware time optimal path parameterization for quadrotors

The increasing popularity of quadrotors has given rise to a class of predominantly vision-driven vehicles. This paper addresses the problem of perception-aware time optimal path parametrization for quadrotors. Although many different choices of perceptual modalities are available, the low weight and power budgets of quadrotor systems makes a camera ideal for on-board navigation and estimation algorithms. However, this does come with a set of challenges. The limited field of view of the camera can restrict the visibility of salient regions in the environment, which dictates the necessity to consider perception and planning jointly. The main contribution of this paper is an efficient time optimal path parametrization algorithm for quadrotors with limited field of view constraints. We show in a simulation study that a state-of-the-art controller can track planned trajectories, and we validate the proposed algorithm on a quadrotor platform in experiments.Comment: Accepted to appear at ICRA 202

Linear Model Predictive Control under Continuous Path Constraints via Parallelized Primal-Dual Hybrid Gradient Algorithm

In this paper, we consider a Model Predictive Control(MPC) problem of a continuous time linear time-invariant system under continuous time path constraints on the states and the inputs. By leveraging the concept of differential flatness, we can replace the differential equations governing the system with linear mapping between the states, inputs and the flat outputs (and their derivatives). The flat output is then parameterized by piecewise polynomials and the model predictive control problem can be equivalently transformed into an Semi-Definite Programming (SDP) problem via Sum-of-Squares with guaranteed constraint satisfaction at every continuous time instant. We further observe that the SDP problem contains a large number of small-size semi-definite matrices as optimization variables, and thus a Primal-Dual Hybrid Gradient (PDHF) algorithm, which can be efficiently parallelized, is developed to accelerate the optimization procedure. Simulation on a quadruple-tank process illustrates that our formulation can guarantee strict constraint satisfaction, while the standard MPC controller based on discretized system may violate the constraint in between a sampling period. On the other hand, we should that the our parallelized PDHG algorithm can outperform commercial solvers for problems with long planning horizon

Receding horizon control of vectored thrust flight experiment

Abstract: The application of a constrained receding horizon control technique to stabilise an indoor vectored-thrust flight experiment, known as the Caltech ducted fan, is given. The receding horizon control problem is formulated as a constrained optimal control problem and solved in real time with an efficient, computational method that combines nonlinear control theory, B-spline basis functions, and nonlinear programming. Characteristic issues, including non-zero computational times, convergence properties, choice of horizon length and terminal cost are discussed. The study validates the applicability of real-time receding horizon control for constrained systems with fast dynamics