Safety in dynamic systems with prevalent uncertainties is crucial. Current robust safe controllers, designed primarily for uni-modal uncertainties, may be either overly conservative or unsafe when handling multi-modal uncertainties. To address the problem, we introduce a novel framework for robust safe control, tailored to accommodate multi-modal Gaussian dynamics uncertainties and control limits. We first present an innovative method for deriving the least conservative robust safe control under additive multi-modal uncertainties. Next, we propose a strategy to identify a locally least-conservative robust safe control under multiplicative uncertainties. Following these, we introduce a unique safety index synthesis method. This provides the foundation for a robust safe controller that ensures a high probability of realizability under control limits and multi-modal uncertainties. Experiments on a simulated Segway validate our approach, showing consistent realizability and less conservatism than controllers designed using uni-modal uncertainty methods. The framework offers significant potential for enhancing safety and performance in robotic applications.

翻译：在充满不确定性的动态系统中，安全性至关重要。当前主要针对单模态不确定性设计的鲁棒安全控制器，在处理多模态不确定性时可能过于保守或不够安全。为解决这一问题，我们提出了一种专门适用于多模态高斯动力学不确定性与控制限制的新型鲁棒安全控制框架。首先，我们提出了一种在加性多模态不确定条件下推导最小保守鲁棒安全控制的创新方法。其次，我们提出了一种策略，可在乘性不确定条件下识别局部最小保守的鲁棒安全控制。在此基础上，我们引入了一种独特的安全指标综合方法。这为鲁棒安全控制器提供了基础，该控制器能在控制限制与多模态不确定性条件下确保高概率的可实现性。在模拟赛格威上的实验验证了该方法，结果表明其始终具备可实现性，且相比采用单模态不确定性方法设计的控制器保守性更低。该框架为提升机器人应用的安全性与性能提供了重要潜力。