Non-linear model predictive control with adaptive time-mesh refinement

Abstract

In this paper, we present a novel solution for realtime, Non-Linear Model Predictive Control (NMPC) exploiting a time-mesh refinement strategy. The proposed controller formulates the Optimal Control Problem (OCP) in terms of flat outputs over an adaptive lattice. In common approximated OCP solutions, the number of discretization points composing the lattice represents a critical upper bound for real-time applications. The proposed NMPC-based technique refines the initially uniform time horizon by adding time steps with a sampling criterion that aims to reduce the discretization error. This enables a higher accuracy in the initial part of the receding horizon, which is more relevant to NMPC, while keeping bounded the number of discretization points. By combining this feature with an efficient Least Square formulation, our solver is also extremely time-efficient, generating trajectories of multiple seconds within only a few milliseconds. The performance of the proposed approach has been validated in a high fidelity simulation environment, by using an UAV platform. We also released our implementation as open source C++ code. * These two authors contribute equally to the work.

Efficient move blocking strategy for multiple shooting‐based non‐linear model predictive control

“…Nonuniform grid schemes are closely related to MB and can also reduce the dimension of (2) by using a denser grid at part of the prediction horizon and a coarser one in the other part of the horizon [1], [10], [4]. For example, as shown in Fig.…”

“…Nonuniform grid schemes suffer from a more coarse state discretization and less accurate predicting trajectory. Although such inaccuracy can be alleviated by using time-mesh refinement techniques [3], [4], [5], [11], additional algorithm complexity and computation burden is introduced. The computational time is also time-varying due to different number of discretizing nodes at each sampling step.…”

“…Since the input MB scheme considers more state and path constraints, its time for solving QP is slightly higher than that of nonuniform grid scheme. It is interesting to compare performance of a specific parameterization of scheme B that shows similar computational time to that of scheme C. This can be achieved by increasing the number of intervals for non-uniform grid NMPC (scheme B) to M = 42 with I =[0, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,28,32,35,37,40,42,44,46,48,50,52,55,60,65,70,75,80] The state and control trajectories are shown in Fig. 4 and the KKT values are shown in Fig.…”

“…To deal with this issue, the number of discretization intervals has been determined a priori off-line while guaranteeing an upper limit of the discretization error in [2]. In addition, adaptive time-mesh refinement techniques have been proposed to improve computation efficiency while maintaining a certain degree of discretization accuracy [3], [4], [5]. The distribution of discretization nodes is adjusted on-line according to specially designed rules and the total number of nodes is bounded.…”

Joint Vision-Based Navigation, Control and Obstacle Avoidance for UAVs in Dynamic Environments

“…In [8] and [22] ACADO, a framework for fast Nonlinear Model Predictive Control (NMPC), is presented; [10] and [21] use ACADO for fast attitude control of UAVs. In our previous work [20], we proposed a solution to improve the real-time capabilities of NMPCs. We aided the controller with a time-mesh strategy that refines the initial part of the horizon inside a flat output formulation.…”