Robust Constrained Learning-based NMPC enabling reliable mobile robot path tracking

文章旨在实现未知干扰下的鲁棒约束、高性能路径跟踪。思路是从简单且高不确定性的过程模型学习准确、低不确定性模型,用VO做定位。与传统约束NMPC不同,本文学习干扰模型加强过程模型,实时应用鲁棒约束。介绍了NMPC、鲁棒约束NMPC、不确定轨迹预测及高斯过程干扰模型等内容。

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Introduction

这篇文章的目的就是achieving robust constrained, high performance path-tracking in spite of unknown disturbances.

这篇文章的思路:simple process model, high model uncertainty →learn\rightarrow^{learn}learnaccurate, low-uncertainty model

这篇文章用VO做Localization.

这篇文章和传统contrained NMPC有如下两方面的不同:

  • 传统方法中process model是预先设计好并且不变的,在这篇文章中learn到disturbance model来加强process model,使得process model可以predict the mean and uncertainty of effects.
  • 传统contrained NMPC没有考虑模型的不确定性,这篇文章apply robust constraints in real time considering the learned uncertainty. We provide robust constraint satisfaction when uncertainty is high and increased performance as uncertainty is reduced through learning.

这篇文章的主要创新点就是:

  1. use learned models
  2. account for model uncertainty

在这里插入图片描述
上面就是本文整体控制框图。RC-LB-NMPC主要包含两个主要的部分:

  • the robust constrained, path-tracking NMPC algorithm based on an a priori process
  • the GP-based disturbance model

Mathematical Formulation

先大概介绍一下NMPC吧:
At a given sample time, NMPC finds a sequence of control inputs that optimizes the plant behavior over a prediction horizon based on current state. The first input in the optimal sequence is then applied to the system. The entire process is repeated at the next sample time for the new system state.

Robust Constrained NMPC
  • 首先肯定是要讲一下状态转移model

The true system is approximate by the sum of an a priori model and an experienced-based, learned model:
xk+1=f(xk,uk)+g(ak)x_{k+1} = f(x_{k}, u_{k}) + g(a_{k})xk+1=f(xk,uk)+g(ak)
where:
f(⋅)f(\cdot)f()——a known nonlinear process model representing our knowledge of ftrue(⋅)f_{true}(\cdot)ftrue()
g(⋅)g(\cdot)g()—— an (initially unknown) disturbance model representing discrepancies between the a priori model and the actual system behavior. g(⋅)g(\cdot)g() is modeled as GP. For simplicity, ak=(xkˉ,uk)a_{k} = (\bar{x_{k}}, u_{k})ak=(xkˉ,uk)

  • 再来讲一下cost function

定义the cost function to be minimized over the next KKK time-steps as:
J(xˉ,u)=(xd−xˉ)TQ(xd−xˉ)+(ud−u)TR(ud−u)J(\bar{x}, u) = (x_{d} - \bar{x})^{T}Q(x_{d} - \bar{x}) + (u_{d} - u)^{T}R(u_{d} - u)J(xˉ,u)=(xdxˉ)TQ(xdxˉ)+(udu)TR(udu)
其中:
QQQ是半正定矩阵,RRR是正定矩阵
xd=(xd,k+1,...,xd,k+K)x_{d} = (x_{d, k+1}, ..., x_{d, k+K})xd=(xd,k+1,...,xd,k+K)——a sequence of desired states
x=(xk+1,...,xk+K)x = (x_{k+1}, ..., x_{k+K})x=(xk+1,...,xk+K)——a sequence of uncertain predicted states, xˉ\bar{x}xˉ is the sequence of mean values based on xxx
ud=(ud,k,...,ud,k+K−1)u_{d} = (u_{d, k}, ..., u_{d, k+K-1})ud=(ud,k,...,ud,k+K1)——a sequence of desired inputs
u=(uk,...,uk+K−1)u = (u_{k}, ..., u_{k+K-1})u=(uk,...,uk+K1)——a sequence of inputs

  • 接下来就是要定义robust constraint了
    从state和input两个角度定义
基于以上基础,我们就可以formulate the following constrained optimization problem:

xopt,uopt=argminx,uJ(xˉ,u){x_{opt}, u_{opt}} = \underset{x,u}{arg min}J(\bar{x}, u)xopt,uopt=x,uargminJ(xˉ,u) subjucttoxˉk+i+1=f(xˉk+i,uk+i)+g(ak+i),i=0,...,K−1subjuct to \bar{x}_{k+i+1} = f(\bar{x}_{k+i} , u_{k+i}) + g(a_{k+i}), i=0, ..., K-1subjucttoxˉk+i+1=f(xˉk+i,uk+i)+g(ak+i),i=0,...,K1 ci(xˉ,u)>0c_{i}(\bar{x}, u) > 0ci(xˉ,u)>0

整个算法的流程:
在这里插入图片描述
在算法收敛之后,we apply the first element of the resulting optimal control input sequence for one time-step, and start all over at the next time-step.

Predicting uncertain trajectories

state都是正态分布的,所以使用Sigma-Point Transform来iteratively predict state sequences.

定义statezi=(xˉk+i,μ(ak+i))∈R2nz_{i} = (\bar{x}_{k+i}, \mu(a_{k+i})) \in R^{2n}zi=(xˉk+i,μ(ak+i))R2n representing the mean state and disturbance at time k+ik+ik+i with uncertainty Pi=diag(∑k+i,∑gp(ak+i))P_{i} = diag(\sum_{k+i}, \sum_{gp}(a_{k+i}))Pi=diag(k+i,gp(ak+i))

这个过程循环K次就可以生成完整的xxx序列。在这种方式下,3σ3\sigma3σ置信区间accouts for uncertainty arising from both localization and modeling

Gaussian Process Disturbance Model

The learned model depends on disturbance observations collection during previous trials.

### 可重构智能表面辅助毫米波无人机通信中的鲁棒与安全传输方案 #### 基于机器学习的方法概述 在可重构智能表面(Reconfigurable Intelligent Surface, RIS)辅助的毫米波无人机通信系统中,采用基于机器学习的技术可以显著提升系统的鲁棒性和安全性。这些技术不仅能够处理复杂的信道条件,还能有效抵御潜在的安全威胁。 #### 信道估计与预测 为了实现高效的通信,在复杂多变的环境中准确地估计和预测信道状态至关重要。通过收集大量历史数据并应用监督学习算法,如支持向量机和支持向量回归,可以构建精确的信道模型[^2]。这有助于提前感知可能发生的干扰情况,并采取预防措施。 #### 波束成形优化 针对毫米波频段特有的短波长特性以及高路径损耗问题,利用深度神经网络来进行自适应波束成形设计成为一种有效的解决方案。具体来说,可以通过训练卷积神经网络来识别最优的发射/接收角度组合,进而最大化链路增益的同时减少旁瓣泄漏带来的负面影响[^1]。 ```python import numpy as np from keras.models import Sequential from keras.layers import Dense, Conv2D, Flatten def create_beamforming_model(input_shape): model = Sequential() # Add convolutional layers to learn spatial features of the channel matrix model.add(Conv2D(32, kernel_size=(3, 3), activation='relu', input_shape=input_shape)) model.add(Flatten()) # Fully connected layer for final beamforming vector prediction model.add(Dense(np.prod(input_shape[:-1]), activation='linear')) return model ``` #### 安全机制强化 考虑到无线通信中存在的窃听风险,引入对抗生成网络(GANs)作为防御手段之一。该方法旨在模拟恶意攻击者的行为模式,并据此调整RIS参数配置以混淆其视线;另一方面,则是借助联邦学习框架下的分布式训练方式保护本地敏感信息不被泄露给中心服务器或其他节点。 #### 实验验证与性能评估 实验结果显示,在不同场景下部署上述策略均能取得良好效果——无论是静态还是移动状态下都能保持较高的吞吐率和服务质量水平;更重要的是,即使面对有意图性的干扰行为也表现出较强的抗扰能力[^4]。
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