用密度函数提升非线性系统的安全控制能力
Safety Critical Model Predictive Control Using Discrete-Time Control Density Functions
- 将控制密度函数融入模型预测控制框架
- 在离散时间下保证系统收敛与安全
- 适合需高安全性控制的机器人场景
本文提出MPC-CDF，一种将控制密度函数（CDF）融入模型预测控制（MPC）框架的新方法，用于保障非线性动力系统中的安全关键控制。通过导航问题的对偶形式，将CDF引入MPC，确保在离散时间设置下的收敛性与安全性。这些密度函数具有物理意义，其相关测度表征系统轨迹的占用情况。基于此占用视角，利用所提出的MPC-CDF框架合成安全关键控制器。通过单车轮模型验证该框架的安全特性，并与基于控制屏障函数的方法进行比较。该方法在水下无人车辆的自主安全导航中得到验证，可有效避开复杂且任意障碍物，实现预期安全水平。
原文摘要 · Abstract (English)
This paper presents MPC-CDF, a new approach integrating control density functions (CDFs) within a model predictive control (MPC) framework to ensure safety-critical control in nonlinear dynamical systems. By using the dual formulation of the navigation problem, we incorporate CDFs into the MPC framework, ensuring both convergence and safety in a discrete-time setting. These density functions are endowed with a physical interpretation, where the associated measure signifies the occupancy of system trajectories. Leveraging this occupancy-based perspective, we synthesize safety-critical controllers using the proposed MPC-CDF framework. We illustrate the safety properties of this framework using a unicycle model and compare it with a control barrier function-based method. The efficacy of this approach is demonstrated in the autonomous safe navigation of an underwater vehicle, which avoids complex and arbitrary obstacles while achieving the desired level of safety.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。