Safe operation of systems such as robots requires them to plan and execute trajectories subject to safety constraints. When those systems are subject to uncertainties in their dynamics, it is challenging to ensure that the constraints are not violated. In this paper, we propose Safe-CDDP, a safe trajectory optimization and control approach for systems under additive uncertainties and non-linear safety constraints based on constrained differential dynamic programming (DDP). The safety of the robot during its motion is formulated as chance constraints with user-chosen probabilities of constraint satisfaction. The chance constraints are transformed into deterministic ones in DDP formulation by constraint tightening. To avoid over-conservatism during constraint tightening, linear control gains of the feedback policy derived from the constrained DDP are used in the approximation of closed-loop uncertainty propagation in prediction. The proposed algorithm is empirically evaluated on three different robot dynamics with up to 12 degrees of freedom in simulation. The computational feasibility and applicability of the approach are demonstrated with a physical hardware implementation.
Wayne State University（韦恩州立大学）；Virginia Tech（弗吉尼亚理工大学）；U.S. Army CCDC Ground Vehicle Systems Center（美国陆军CCDC地面车辆系统中心）；Aptiv（安波福）
Significant advances in sensing, robotics, and wireless networks have enabled the collaborative utilization of autonomous aerial, ground and underwater vehicles for various applications. However, to successfully harness the benefits of these unmanned ground vehicles (UGVs) in homeland security operations, it is critical to efficiently solve UGV path planning problem which lies at the heart of these operations. Furthermore, in the real-world applications of UGVs, these operations encounter uncertainties such as incomplete information about the target sites, travel times, and the availability of…
School of Electrical and Computer Engineering（电气与计算机工程学院）；King Fahd University of Petroleum & Minerals（法赫德国王石油与矿产大学）；School of Computer Science（计算机科学学院）；George W. Woodruff School of Mechanical Engineering（乔治·W·伍德拉夫机械工程学院）；Daniel Guggenheim School of Aerospace Engineering（丹尼尔·古根海姆航空航天工程学院）
Certified safe control is a growing challenge in robotics, especially when performance and safety objectives must be concurrently achieved. In this work, we extend the barrier state (BaS) concept, recently proposed for safe stabilization of continuous time systems, to safety embedded trajectory optimization for discrete time systems using discrete barrier states (DBaS). The constructed DBaS is embedded into the discrete model of the safety-critical system integrating safety objectives into the system's dynamics and performance objectives. Thereby, the control policy is directly supplied by saf…
Katholieke Universiteit Leuven（鲁汶天主教大学）；University of Melbourne（墨尔本大学）
We propose a safety-guaranteed planning and control framework for unmanned surface vessels (USVs), using Gaussian processes (GPs) to learn uncertainties. The uncertainties encountered by USVs, including external disturbances and model mismatches, are potentially state-dependent, time-varying, and hard to capture with constant models. GP is a powerful learning-based tool that can be integrated with a model-based planning and control framework, which employs a Hamilton-Jacobi differential game formulation. Such a combination yields less conservative trajectories and safety-guaranteeing control s…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Stanford University（斯坦福大学）
Trajectory planning under uncertainty is an active research topic. Previous works predict state and state estimation uncertainties along trajectories to check for collision safety. They assume either stochastic or bounded sensing uncertainties. However, GNSS pseudoranges are typically modeled to contain stochastic uncertainties with additional biases in urban environments. Thus, given bounds for the bias, the planner needs to account for both stochastic and bounded sensing uncertainties. In our prior work we presented a reachability analysis to predict state and state estimation uncertainties …
University of Pennsylvania（宾夕法尼亚大学）；Purdue University（普渡大学）
We propose a Safe Pontryagin Differentiable Programming (Safe PDP) methodology, which establishes a theoretical and algorithmic framework to solve a broad class of safety-critical learning and control tasks -- problems that require the guarantee of safety constraint satisfaction at any stage of the learning and control progress. In the spirit of interior-point methods, Safe PDP handles different types of system constraints on states and inputs by incorporating them into the cost or loss through barrier functions. We prove three fundamentals of the proposed Safe PDP: first, both the solution an…
School of Electronics and Information Technology, Sun Yat-sen University（中山大学电子与信息工程学院）；School of Data and Computer Science, Sun Yat-sen University（中山大学数据与计算机学院）
Safety and tracking stability are crucial for safety-critical systems such as self-driving cars, autonomous mobile robots, industrial manipulators. To efficiently control safety-critical systems to ensure their safety and achieve tracking stability, accurate system dynamic models are usually required. However, accurate system models are not always available in practice. In this paper, a learning-based safety-stability-driven control (LBSC) algorithm is presented to guarantee the safety and tracking stability for nonlinear safety-critical systems subject to control input constraints under model…
Control Barrier Functions (CBF) are widely used to enforce the safety-critical constraints on nonlinear systems. Recently, these functions are being incorporated into a path planning framework to design safety-critical path planners. However, these methods fall short of providing a realistic path considering both the algorithm's run-time complexity and enforcement of the safety-critical constraints. This paper proposes a novel motion planning approach using the well-known Rapidly Exploring Random Trees (RRT) algorithm that enforces both CBF and the robot Kinodynamic constraints to generate a s…
Model mismatches prevail in real-world applications. Ensuring safety for systems with uncertain dynamic models is critical. However, existing robust safe controllers may not be realizable when control limits exist. And existing methods use loose over-approximation of uncertainties, leading to conservative safe controls. To address these challenges, we propose a control-limits aware robust safe control framework for bounded state-dependent uncertainties. We propose safety index synthesis to find a robust safe controller guaranteed to be realizable under control limits. And we solve for robust s…
Maintaining safety under adaptation has long been considered to be an important capability for autonomous systems. As these systems estimate and change the ego-model of the system dynamics, questions regarding how to develop safety guarantees for such systems continue to be of interest. We propose a novel robust safe control methodology that uses set-based safety constraints to make a robotic system with dynamical uncertainties safely adapt and operate in its environment. The method consists of designing a scalar energy function (safety index) for an adaptive system with parametric uncertainty…
Input-to-State Safe Backstepping: Robust Safety-Critical Control with Unmatched Uncertainties
Department of Electrical and Computer Engineering, North Carolina State University（电气与计算机工程系，北卡罗来纳州立大学）；Department of Mechanical and Civil Engineering, California Institute of Technology（机械与土木工程系，加州理工学院）
Computer Science and Artificial Intelligence Laboratory (CSAIL)（计算机科学与人工智能实验室（CSAIL））；Massachusetts Institute of Technology (MIT)（麻省理工学院（MIT））
In this paper, we address the real-time risk-bounded safety verification problem of continuous-time state trajectories of autonomous systems in the presence of uncertain time-varying nonlinear safety constraints. Risk is defined as the probability of not satisfying the uncertain safety constraints. Existing approaches to address the safety verification problems under uncertainties either are limited to particular classes of uncertainties and safety constraints, e.g., Gaussian uncertainties and linear constraints, or rely on sampling based methods. In this paper, we provide a fast convex algori…
Stanford University（斯坦福大学）；NASA Ames Research Center（NASA艾姆斯研究中心）
An open question in autonomous driving is how best to use simulation to validate the safety of autonomous vehicles. Existing techniques rely on simulated rollouts, which can be inefficient for finding rare failure events, while other techniques are designed to only discover a single failure. In this work, we present a new safety validation approach that attempts to estimate the distribution over failures of an autonomous policy using approximate dynamic programming. Knowledge of this distribution allows for the efficient discovery of many failure examples. To address the problem of scalability…
The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；University of Verona（维罗纳大学）；The Weizmann Institute of Science（魏茨曼科学研究所）
Deep reinforcement learning (DRL) has achieved groundbreaking successes in a wide variety of robotic applications. A natural consequence is the adoption of this paradigm for safety-critical tasks, where human safety and expensive hardware can be involved. In this context, it is crucial to optimize the performance of DRL-based agents while providing guarantees about their behavior. This paper presents a novel technique for incorporating domain-expert knowledge into a constrained DRL training loop. Our technique exploits the scenario-based programming paradigm, which is designed to allow specify…
VisionSafeEnhanced VPC: Cautious Predictive Control with Visibility Constraints under Uncertainty for Autonomous Robotic Surgery
School of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）；School of Advanced Manufacturing and Robotics, Peking University（北京大学先进制造与机器人学院）；MicroPort MedBot (Group) Company Ltd.（微宏医疗机器人（集团）有限公司）；Department of Biomedical Engineering, City University of Hong Kong（香港城市大学生物医学工程系）
Tolerance estimation problems are prevailing in engineering applications. For example, in modern robotics, it remains challenging to efficiently estimate joint tolerance, \ie the maximal allowable deviation from a reference robot state such that safety constraints are still satisfied. This paper presented an efficient algorithm to estimate the joint tolerance using sum-of-squares programming. It is theoretically proved that the algorithm provides a tight lower bound of the joint tolerance. Extensive numerical studies demonstrate that the proposed method is computationally efficient and near op…
We present an online and data-driven uncertainty quantification method to enable the development of safe human-robot collaboration applications. Safety and risk assessment of systems are strongly correlated with the accuracy of measurements: Distinctive parameters are often not directly accessible via known models and must therefore be measured. However, measurements generally suffer from uncertainties due to the limited performance of sensors, even unknown environmental disturbances, or humans. In this work, we quantify these measurement uncertainties by making use of conservation measures wh…
The Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）
Safe navigation in real-time is challenging because engineers need to work with uncertain vehicle dynamics, variable external disturbances, and imperfect controllers. A common safety strategy is to inflate obstacles by hand-defined margins. However, arbitrary static margins often fail in more dynamic scenarios, and using worst-case assumptions is overly conservative for most settings where disturbances over time. In this work, we propose a middle ground: safety margins that adapt on-the-fly. In an offline phase, we use Monte Carlo simulations to pre-compute a library of safety margins for mult…
Robots operating in real world settings must navigate and maintain safety while interacting with many heterogeneous agents and obstacles. Multi-Agent Control Barrier Functions (CBF) have emerged as a computationally efficient tool to guarantee safety in multi-agent environments, but they assume perfect knowledge of both the robot dynamics and other agents' dynamics. While knowledge of the robot's dynamics might be reasonably well known, the heterogeneity of agents in real-world environments means there will always be considerable uncertainty in our prediction of other agents' dynamics. This wo…
This paper considers safe robot mission planning in uncertain dynamical environments. This problem arises in applications such as surveillance, emergency rescue, and autonomous driving. It is a challenging problem due to modeling and integrating dynamical uncertainties into a safe planning framework, and finding a solution in a computationally tractable way. In this work, we first develop a probabilistic model for dynamical uncertainties. Then, we provide a framework to generate a path that maximizes safety for complex missions by incorporating the uncertainty model. We also devise a Monte Car…
Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers
The Hong Kong University of Science and Technology（香港科学与技术大学）；National University of Singapore（新加坡国立大学）；Department of Electrical and Computer Engineering（电气与计算机工程系）
FiveAI Ltd（FiveAI有限公司）；University of Oxford（牛津大学）；University of Edinburgh（爱丁堡大学）
Recent road trials have shown that guaranteeing the safety of driving decisions is essential for the wider adoption of autonomous vehicle technology. One promising direction is to pose safety requirements as planning constraints in nonlinear, non-convex optimization problems of motion synthesis. However, many implementations of this approach are limited by uncertain convergence and local optimality of the solutions achieved, affecting overall robustness. To improve upon these issues, we propose a novel two-stage optimization framework: in the first stage, we find a solution to a Mixed-Integer …
Aarhus University（奥胡斯大学）；University of Southern Denmark（南丹麦大学）
This paper is an extension to an early presented programming language, called a domain specific language. This paper extends the proposed concept with new sensors and behaviours to address real-life situations. The functionality was tested in lab experiments, and an extension to the earlier concepts is proposed.
Tsinghua University（清华大学）；Harvard University（哈佛大学）；University of Science and Technology Beijing（北京科技大学）
Safe reinforcement learning (RL) that solves constraint-satisfactory policies provides a promising way to the broader safety-critical applications of RL in real-world problems such as robotics. Among all safe RL approaches, model-based methods reduce training time violations further due to their high sample efficiency. However, lacking safety robustness against the model uncertainties remains an issue in safe model-based RL, especially in training time safety. In this paper, we propose a distributional reachability certificate (DRC) and its Bellman equation to address model uncertainties and c…
Uncertainties in Deep Neural Network (DNN)-based perception and vehicle's motion pose challenges to the development of safe autonomous driving vehicles. In this paper, we propose a safe motion planning framework featuring the quantification and propagation of DNN-based perception uncertainties and motion uncertainties. Contributions of this work are twofold: (1) A Bayesian Deep Neural network model which detects 3D objects and quantitatively captures the associated aleatoric and epistemic uncertainties of DNNs; (2) An uncertainty-aware motion planning algorithm (PU-RRT) that accounts for uncer…
