在先前有关多代理区防御游戏的文献中，捍卫者对攻击者的任务是基于与攻击者拦截相关的成本度量完成的。与此相反，本文提出了一项互相碰撞拦截策略（IDCAI），供捍卫者拦截攻击者以捍卫保护区，因此辩护人到攻击者的分配协议不仅要考虑到拦截 - 相关的成本，但也考虑了捍卫者在其最佳拦截轨迹上的任何未来碰撞。特别是，在本文中，捍卫者被分配给使用混合成员二次计划（MIQP）拦截攻击者，该计划：1）最大程度地减少后卫在时间优势控制下捕获攻击者所花费的时间，以及2 ）有助于消除或延迟捍卫者在最佳轨迹上的未来碰撞。为了防止由于攻击者的时间次数最佳行为而引起的最佳轨迹或碰撞的必然碰撞，还提供了使用指数控制屏障功能（ECBF）的最小增强控制。模拟显示了该方法的功效。

尽管动态游戏为建模代理的互动提供了丰富的范式，但为现实世界应用程序解决这些游戏通常具有挑战性。许多现实的交互式设置涉及一般的非线性状态和输入约束，它们彼此之间的决策相结合。在这项工作中，我们使用约束的游戏理论框架开发了一个高效且快速的计划者，用于在受限设置中进行交互式计划。我们的关键见解是利用代理的目标和约束功能的特殊结构，这些功能在多代理交互中进行快速和可靠的计划。更确切地说，我们确定了代理成本功能的结构，在该结构下，由此产生的动态游戏是受约束潜在动态游戏的实例。受限的潜在动态游戏是一类游戏，而不是解决一组耦合的约束最佳控制问题，而是通过解决单个约束最佳控制问题来找到NASH平衡。这简化了限制的交互式轨迹计划。我们比较了涉及四个平面代理的导航设置中方法的性能，并表明我们的方法平均比最先进的速度快20倍。我们进一步在涉及一个四型和两个人的导航设置中对我们提出的方法提供了实验验证。

We develop a new framework for trajectory planning on predefined paths, for general N-link manipulators. Different from previous approaches generating open-loop minimum time controllers or pre-tuned motion profiles by time-scaling, we establish analytic algorithms that recover all initial conditions that can be driven to the desirable target set while adhering to environment constraints. More technologically relevant, we characterise families of corresponding safe state-feedback controllers with several desirable properties. A key enabler in our framework is the introduction of a state feedback template, that induces ordering properties between trajectories of the resulting closed-loop system. The proposed structure allows working on the nonlinear system directly in both the analysis and synthesis problems. Both offline computations and online implementation are scalable with respect to the number of links of the manipulator. The results can potentially be used in a series of challenging problems: Numerical experiments on a commercial robotic manipulator demonstrate that efficient online implementation is possible.

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.

In this work, we propose a collision-free source seeking control framework for unicycle robots traversing an unknown cluttered environment. In this framework, the obstacle avoidance is guided by the control barrier functions (CBF) embedded in quadratic programming and the source seeking control relies solely on the use of on-board sensors that measure signal strength of the source. To tackle the mixed relative degree of the CBF, we proposed three different CBF, namely the zeroing control barrier functions (ZCBF), exponential control barrier functions (ECBF), and reciprocal control barrier functions (RCBF) that can directly be integrated with our recent gradient-ascent source-seeking control law. We provide rigorous analysis of the three different methods and show the efficacy of the approaches in simulations using Matlab, as well as, using a realistic dynamic environment with moving obstacles in Gazebo/ROS.

Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and with a view toward automotive applications, this paper develops a methodology that allows safety conditions-expressed as control barrier functionsto be unified with performance objectives-expressed as control Lyapunov functions-in the context of real-time optimizationbased controllers. Safety conditions are specified in terms of forward invariance of a set, and are verified via two novel generalizations of barrier functions; in each case, the existence of a barrier function satisfying Lyapunov-like conditions implies forward invariance of the set, and the relationship between these two classes of barrier functions is characterized. In addition, each of these formulations yields a notion of control barrier function (CBF), providing inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). The mediation of safety and performance through a QP is demonstrated on adaptive cruise control and lane keeping, two automotive control problems that present both safety and performance considerations coupled with actuator bounds.

本文涉及专业示范的学习安全控制法。我们假设系统动态和输出测量图的适当模型以及相应的错误界限。我们首先提出强大的输出控制屏障功能（ROCBF）作为保证安全的手段，通过控制安全集的前向不变性定义。然后，我们提出了一个优化问题，以从展示安全系统行为的专家演示中学习RocBF，例如，从人类运营商收集的数据。随着优化问题，我们提供可验证条件，可确保获得的Rocbf的有效性。这些条件在数据的密度和学习函数的LipsChitz和Lipshitz和界限常数上说明，以及系统动态和输出测量图的模型。当ROCBF的参数化是线性的，然后，在温和的假设下，优化问题是凸的。我们在自动驾驶模拟器卡拉验证了我们的调查结果，并展示了如何从RGB相机图像中学习安全控制法。

我们研究了覆盖的阶段 - 避免多个代理的动态游戏，其中多个代理相互作用，并且每种希望满足不同的目标条件，同时避免失败状态。 Reach-避免游戏通常用于表达移动机器人运动计划中发现的安全关键最优控制问题。虽然这些运动计划问题存在各种方法，但我们专注于找到时间一致的解决方案，其中计划未来的运动仍然是最佳的，尽管先前的次优行动。虽然摘要，时间一致性封装了一个非常理想的财产：即使机器人早期从计划发出的机器人的运动发散，即，由于例如内在的动态不确定性或外在环境干扰，即使机器人的运动分歧，时间一致的运动计划也保持最佳。我们的主要贡献是一种计算 - 避免多种代理的算法算法，避免呈现时间一致的解决方案。我们展示了我们在两位和三位玩家模拟驾驶场景中的方法，其中我们的方法为所有代理商提供了安全控制策略。

游戏理论到目前为止在各个领域都发现了许多应用，包括经济学，工业，法学和人工智能，每个玩家都只关心自己对非合作或合作方式的兴趣，但对其他玩家没有明显的恶意。但是，在许多实际应用中，例如扑克，国际象棋，逃避者追求，毒品拦截，海岸警卫队，网络安全和国防，球员通常都具有对抗性立场，也就是说，每个球员的自私行动不可避免地或故意造成损失或对其他球员造成严重破坏。沿着这条线，本文对在对抗性游戏中广泛使用的三种主要游戏模型（即零和零正常形式和广泛形式游戏，stackelberg（Security）游戏，零和差异游戏）提供了系统的调查。观点，包括游戏模型的基本知识，（近似）平衡概念，问题分类，研究前沿，（近似）最佳策略寻求技术，普遍的算法和实际应用。最后，还讨论了有关对抗性游戏的有希望的未来研究方向。

安全限制和最优性很重要，但有时控制器有时相互冲突的标准。虽然这些标准通常与不同的工具单独解决以维持正式保障，但在惩罚失败时，加强学习的常见做法是惩罚，以惩罚为单纯的启发式。我们严格地检查了安全性和最优性与惩罚的关系，并对安全价值函数进行了足够的条件：对给定任务的最佳价值函数，并强制执行安全约束。我们通过强大的二元性证明，揭示这种关系的结构，表明始终存在一个有限的惩罚，引起安全值功能。这种惩罚并不是独特的，但大不束缚：更大的惩罚不会伤害最优性。虽然通常无法计算最低所需的惩罚，但我们揭示了清晰的惩罚，奖励，折扣因素和动态互动的结构。这种洞察力建议实用，理论引导的启发式设计奖励功能，用于控制安全性很重要的控制问题。

本文介绍了一个新颖的社会偏好意识分散的安全控制框架，以解决避免多机构碰撞的责任分配问题。考虑到代理不一定会以对称方式进行合作，本文着重于具有不同合作水平的异质代理之间的半合作行为。利用社会价值取向（SVO）来量化个人自私的思想，我们提出了一个新颖的责任相关社会价值取向（R-SVO）的新颖概念，以表达成对代理之间的预期相对社会含义。这用于根据相应的责任份额来重新定义每个代理商的社会偏好或个性，以促进协调方案，例如所有代理商以不对称方式互动的半合件碰撞避免。通过通过拟议的本地成对责任权重纳入这种相对的社会影响，我们为个人代理人开发了与责任相关的控制屏障功能的安全控制框架，并通过正式可证明的安全保证可以实现多代理碰撞的避免。提供了模拟来证明在多个多代理导航任务中所提出的框架的有效性和效率，例如位置交换游戏，自动驾驶汽车公路公路坡道合并方案以及圆形交换游戏。

Learning-enabled control systems have demonstrated impressive empirical performance on challenging control problems in robotics, but this performance comes at the cost of reduced transparency and lack of guarantees on the safety or stability of the learned controllers. In recent years, new techniques have emerged to provide these guarantees by learning certificates alongside control policies -- these certificates provide concise, data-driven proofs that guarantee the safety and stability of the learned control system. These methods not only allow the user to verify the safety of a learned controller but also provide supervision during training, allowing safety and stability requirements to influence the training process itself. In this paper, we provide a comprehensive survey of this rapidly developing field of certificate learning. We hope that this paper will serve as an accessible introduction to the theory and practice of certificate learning, both to those who wish to apply these tools to practical robotics problems and to those who wish to dive more deeply into the theory of learning for control.

本文考虑了安全协调一个配备传感器的机器人团队的问题，以减少有关动态过程的不确定性，而该过程将使目标消除信息增益和能源成本。优化这种权衡是可取的，但是在机器人轨迹集中导致非占主酮目标函数。因此，基于协调下降的普通多机器人计划者失去了其性能保证。此外，处理非单调性的方法在受到机器人间碰撞避免约束时会失去其性能保证。由于需要保留性能保证和安全保证，这项工作提出了一种分布式计划者的层次结构方法，该方法使用本地搜索，并根据控制屏障功能提供了基于控制屏障功能的当地搜索和分散的控制器，以确保安全并鼓励及时到达传感位置。通过大量的模拟，硬件测试和硬件实验，我们证明了所提出的方法比基于坐标下降的算法在感应和能源成本之间取得更好的权衡。

We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. The intruders' objective is to breach the target boundary without being captured by the defender. As soon as the current intruder breaches the target or gets captured by the defender, the next intruder appears at a random location on a fixed circle surrounding the target. Therefore, the defender's final location at the end of the current game becomes its initial location for the next game. Thus, the players pick strategies that are advantageous for the current as well as for the future games. Depending on the information available to the players, each game is divided into two phases: partial information and full information phase. Under some assumptions on the sensing and speed capabilities, we analyze the agents' strategies in both phases. We derive equilibrium strategies for both the players to optimize the capture percentage using the notions of engagement surface and capture circle. We quantify the percentage of capture for both finite and infinite sequences of incoming intruders.

We propose a path planning methodology for a mobile robot navigating through an obstacle-filled environment to generate a reference path that is traceable with moderate sensing efforts. The desired reference path is characterized as the shortest path in an obstacle-filled Gaussian belief manifold equipped with a novel information-geometric distance function. The distance function we introduce is shown to be an asymmetric quasi-pseudometric and can be interpreted as the minimum information gain required to steer the Gaussian belief. An RRT*-based numerical solution algorithm is presented to solve the formulated shortest-path problem. To gain insight into the asymptotic optimality of the proposed algorithm, we show that the considered path length function is continuous with respect to the topology of total variation. Simulation results demonstrate that the proposed method is effective in various robot navigation scenarios to reduce sensing costs, such as the required frequency of sensor measurements and the number of sensors that must be operated simultaneously.

Many autonomous agents, such as intelligent vehicles, are inherently required to interact with one another. Game theory provides a natural mathematical tool for robot motion planning in such interactive settings. However, tractable algorithms for such problems usually rely on a strong assumption, namely that the objectives of all players in the scene are known. To make such tools applicable for ego-centric planning with only local information, we propose an adaptive model-predictive game solver, which jointly infers other players' objectives online and computes a corresponding generalized Nash equilibrium (GNE) strategy. The adaptivity of our approach is enabled by a differentiable trajectory game solver whose gradient signal is used for maximum likelihood estimation (MLE) of opponents' objectives. This differentiability of our pipeline facilitates direct integration with other differentiable elements, such as neural networks (NNs). Furthermore, in contrast to existing solvers for cost inference in games, our method handles not only partial state observations but also general inequality constraints. In two simulated traffic scenarios, we find superior performance of our approach over both existing game-theoretic methods and non-game-theoretic model-predictive control (MPC) approaches. We also demonstrate our approach's real-time planning capabilities and robustness in two hardware experiments.

本文开发了一种基于模型的强化学习（MBR）框架，用于在线在线学习无限范围最佳控制问题的价值函数，同时遵循表示为控制屏障功能（CBFS）的安全约束。我们的方法是通过开发一种新型的CBFS，称为Lyapunov样CBF（LCBF），其保留CBFS的有益特性，以开发最微创的安全控制政策，同时也具有阳性半自动等所需的Lyapunov样品质 - 义法。我们展示这些LCBFS如何用于增强基于学习的控制策略，以保证安全性，然后利用这种方法在MBRL设置中开发安全探索框架。我们表明，我们的开发方法可以通过各种数值示例来处理比较法的更通用的安全限制。

对于多面体之间的障碍物躲避开发的控制器是在狭小的空间导航一个具有挑战性的和必要的问题。传统的方法只能制定的避障问题，因为离线优化问题。为了应对这些挑战，我们提出用非光滑控制屏障功能多面体之间的避障，它可以实时与基于QP的优化问题来解决基于二元安全关键最优控制。一种双优化问题被引入到表示被施加到构造控制屏障功能多面体和用于双形式的拉格朗日函数之间的最小距离。我们验证了避开障碍物与在走廊环境受控的L形（沙发形）机器人建议的双配制剂。据我们所知，这是第一次，实时紧避障与非保守的演习是在移动沙发（钢琴）与非线性动力学问题来实现的。

游戏理论运动计划者是控制多个高度交互式机器人系统的有效解决方案。大多数现有的游戏理论规划师不切实际地假设所有代理都可以使用先验的目标功能知识。为了解决这个问题，我们提出了一个容忍度的退缩水平游戏理论运动计划者，该计划者利用了与意图假设的可能性相互交流。具体而言，机器人传达其目标函数以结合意图。离散的贝叶斯过滤器旨在根据观察到的轨迹与传达意图的轨迹之间的差异来实时推断目标。在仿真中，我们考虑了三种安全至关重要的自主驾驶场景，即超车，车道交叉和交叉点，以证明我们计划者在存在通信网络中存在错误的传输情况下利用替代意图假设来产生安全轨迹的能力。

在本文中，我们提出了针对无人接地车辆（UGV）的新的控制屏障功能（CBF），该功能有助于避免与运动学（非零速度）障碍物发生冲突。尽管当前的CBF形式已经成功地保证了与静态障碍物的安全/碰撞避免安全性，但动态案例的扩展已获得有限的成功。此外，借助UGV模型，例如Unicycle或自行车，现有CBF的应用在控制方面是保守的，即在某些情况下不可能进行转向/推力控制。从经典的碰撞锥中汲取灵感来避免轨迹规划，我们介绍了其新颖的CBF配方，并具有对独轮车和自行车模型的安全性保证。主要思想是确保障碍物的速度W.R.T.车辆总是指向车辆。因此，我们构建了一个约束，该约束确保速度向量始终避开指向车辆的向量锥。这种新控制方法的功效在哥白尼移动机器人上进行了实验验证。我们将其进一步扩展到以自行车模型的形式扩展到自动驾驶汽车，并在Carla模拟器中的各种情况下证明了避免碰撞。