Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained stochastic optimal control with dynamics learning and feedback control. We derive an iterative convex optimization algorithm that solves an \underline{Info}rmation-cost \underline{S}tochastic \underline{N}onlinear \underline{O}ptimal \underline{C}ontrol problem (Info-SNOC). The optimization objective encodes control cost for performance and exploration cost for learning, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust regression model that is learned from data. The Info-SNOC algorithm is used to compute a sub-optimal pool of safe motion plans that aid in exploration for learning unknown residual dynamics under safety constraints. A stable feedback controller is used to execute the motion plan and collect data for model learning. We prove the safety of rollout from our exploration method and reduction in uncertainty over epochs, thereby guaranteeing the consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot. We demonstrate that our approach has higher success rate in ensuring safety when compared to a deterministic trajectory optimization approach.
University of California San Diego（加州大学圣地亚哥分校）；San Diego State University（圣地亚哥州立大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Safety is a critical concern for the success of urban air mobility, especially in dynamic and uncertain environments. This paper proposes a path planning algorithm based on RRT in conjunction with chance constraints in the presence of uncertain obstacles. The chance-constrained formulation for Gaussian distributed obstacles is developed by converting the probabilistic constraints to deterministic constraints in terms of distribution parameters. The probabilistic feasible region at every time step can be established through the simulation of the system state and the evaluation of convex constra…
Many practical applications of robotics require systems that can operate safely despite uncertainty. In the context of motion planning, two types of uncertainty are particularly important when planning safe robot trajectories. The first is environmental uncertainty -- uncertainty in the locations of nearby obstacles, stemming from sensor noise or (in the case of obstacles' future locations) prediction error. The second class of uncertainty is uncertainty in the robots own state, typically caused by tracking or estimation error. To achieve high levels of safety, it is necessary for robots to co…
IIIT Hyderabad（印度海得拉巴国际信息技术学院）；University of Tartu（塔尔图大学）
We present CCO-VOXEL: the very first chance-constrained optimization (CCO) algorithm that can compute trajectory plans with probabilistic safety guarantees in real-time directly on the voxel-grid representation of the world. CCO-VOXEL maps the distribution over the distance to the closest obstacle to a distribution over collision-constraint violation and computes an optimal trajectory that minimizes the violation probability. Importantly, unlike existing works, we never assume the nature of the sensor uncertainty or the probability distribution of the resulting collision-constraint violations.…
University of Luxembourg（卢森堡大学）；Interdisciplinary Centre for Security, Reliability and Trust（安全、可靠性与信任跨学科中心）；ispace Europe（ispace欧洲公司）
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an obstacle's space: a polyhedron, such as a cuboid, or a nonlinear differentiable surface, such as an ellipsoid. The former approach relies on disjunctive programming, which has a relatively high computational cost that grows exponentially with the number of obstacles. The latter approach needs to be linearized locally to find a tractable evaluation of the chance co…
This paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem via a Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). Through Lagrangian relaxation, we convert the chance-constrained (risk-constrained) SOC problem to a risk-minimizing SOC problem, the cost function of which possesses the time-additive Bellman structure. We show that the risk-minimizing control synthesis is equivalent to solving an HJB PDE whose boundary condition can be tuned appropriately to achieve a desired level of safety. Furthermore, it is shown that …
We propose a method for learning constraints represented as Gaussian processes (GPs) from locally-optimal demonstrations. Our approach uses the Karush-Kuhn-Tucker (KKT) optimality conditions to determine where on the demonstrations the constraint is tight, and a scaling of the constraint gradient at those states. We then train a GP representation of the constraint which is consistent with and which generalizes this information. We further show that the GP uncertainty can be used within a kinodynamic RRT to plan probabilistically-safe trajectories, and that we can exploit the GP structure withi…
In this paper, we address the problem of sampling-based motion planning under motion and measurement uncertainty with probabilistic guarantees. We generalize traditional sampling-based tree-based motion planning algorithms for deterministic systems and propose belief-$\mathcal{A}$, a framework that extends any kinodynamical tree-based planner to the belief space for linear (or linearizable) systems. We introduce appropriate sampling techniques and distance metrics for the belief space that preserve the probabilistic completeness and asymptotic optimality properties of the underlying planner. W…
Tsinghua University（清华大学）；Shanghai Qizhi Institute（上海期智研究院）；University of California, Berkeley（加州大学伯克利分校）；University of Tokyo（东京大学）
Motion planning under uncertainty is of significant importance for safety-critical systems such as autonomous vehicles. Such systems have to satisfy necessary constraints (e.g., collision avoidance) with potential uncertainties coming from either disturbed system dynamics or noisy sensor measurements. However, existing motion planning methods cannot efficiently find the robust optimal solutions under general nonlinear and non-convex settings. In this paper, we formulate such problem as chance-constrained Gaussian belief space planning and propose the constrained iterative Linear Quadratic Gaus…
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…
Autonomous Systems Lab, ETH Zürich（苏黎世联邦理工学院自主系统实验室）
In order to enable Micro-Aerial Vehicles (MAVs) to assist in complex, unknown, unstructured environments, they must be able to navigate with guaranteed safety, even when faced with a cluttered environment they have no prior knowledge of. While trajectory optimization-based local planners have been shown to perform well in these cases, prior work either does not address how to deal with local minima in the optimization problem, or solves it by using an optimistic global planner. We present a conservative trajectory optimization-based local planner, coupled with a local exploration strategy that…
Continuous-Time Gaussian Belief Trees for Motion Planning
Department of Aerospace Engineering Sciences at the University of Colorado Boulder（科罗拉多大学博尔德分校航空航天工程科学系）；Department of Aerospace and Ocean Engineering at Virginia Tech（弗吉尼亚理工学院航空航天与海洋工程系）
ETH Zürich（苏黎世联邦理工学院）；Technical University of Munich（慕尼黑工业大学）；Google（谷歌）
Exploration of unknown environments is a fundamental problem in robotics and an essential component in numerous applications of autonomous systems. A major challenge in exploring unknown environments is that the robot has to plan with the limited information available at each time step. While most current approaches rely on heuristics and assumption to plan paths based on these partial observations, we instead propose a novel way to integrate deep learning into exploration by leveraging 3D scene completion for informed, safe, and interpretable exploration mapping and planning. Our approach, SC…
Safety is essential for reinforcement learning (RL) applied in the real world. Adding chance constraints (or probabilistic constraints) is a suitable way to enhance RL safety under uncertainty. Existing chance-constrained RL methods like the penalty methods and the Lagrangian methods either exhibit periodic oscillations or learn an over-conservative or unsafe policy. In this paper, we address these shortcomings by proposing a separated proportional-integral Lagrangian (SPIL) algorithm. We first review the constrained policy optimization process from a feedback control perspective, which regard…
Wasserstein Distributionally Robust Chance Constrained Trajectory Optimization for Mobile Robots within Uncertain Safe Corridor
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology（华中科技大学人工智能与自动化学院）；School of Data Science, City University of Hong Kong（香港城市大学数据科学学院）
Contextual Robotics Institute（情境机器人研究所）；University of California San Diego（加州大学圣地亚哥分校）
This paper considers enforcing safety and stability of dynamical systems in the presence of model uncertainty. Safety and stability constraints may be specified using a control barrier function (CBF) and a control Lyapunov function (CLF), respectively. To take model uncertainty into account, robust and chance formulations of the constraints are commonly considered. However, this requires known error bounds or a known distribution for the model uncertainty, and the resulting formulations may suffer from over-conservatism or over-confidence. In this paper, we assume that only a finite set of mod…
Learning Safe Control via On-the-Fly Bandit Exploration
Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）；TUM School of Computation, Information and Technology, Technical University of Munich（慕尼黑技术大学计算、信息与技术学院）
Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are incorporated into the planning problem to provide probabilistic safety guarantees by imposing an upper bound on the collision probability of the planned trajectory. Yet, this results in overly conservative behavior on the grounds that the gap between the obtained risk and the specified upper limit is not explicitly restricted. To address this issue, we propose…
Many collaborative human-robot tasks require the robot to stay safe and work efficiently around humans. Since the robot can only stay safe with respect to its own model of the human, we want the robot to learn a good model of the human in order to act both safely and efficiently. This paper studies methods that enable a robot to safely explore the space of a human-robot system to improve the robot's model of the human, which will consequently allow the robot to access a larger state space and better work with the human. In particular, we introduce active exploration under the framework of ener…
SHAPO: Sharpness-Aware Policy Optimization for Safe Exploration
Université de Montréal（蒙特利尔大学）；Mila - Québec AI Institute（蒙特利尔人工智能研究所）；Université Laval（拉瓦尔大学）；IID - Institut Intelligence et Données（智能与数据研究所）；LawZero；CIFAR AI Chair（CIFAR人工智能主席）
Laboratory of Information and Decision Systems, Massachusetts Institute of Technology（麻省理工学院信息与决策系统实验室）
In autonomous Mobility on Demand (MOD) systems, customers request rides from a fleet of shared vehicles that can be automatically positioned in response to customer demand. Recent approaches to MOD systems have focused on environments where customers can only request rides through an app or by waiting at a station. This paper develops MOD fleet management approaches for ride hailing, where customers may instead request rides simply by hailing a passing vehicle, an approach of particular importance for campus MOD systems. The challenge for ride hailing is that customer demand is not explicitly …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；University of California Berkeley（加州大学伯克利分校）
Safe exploration presents a major challenge in reinforcement learning (RL): when active data collection requires deploying partially trained policies, we must ensure that these policies avoid catastrophically unsafe regions, while still enabling trial and error learning. In this paper, we target the problem of safe exploration in RL by learning a conservative safety estimate of environment states through a critic, and provably upper bound the likelihood of catastrophic failures at every training iteration. We theoretically characterize the tradeoff between safety and policy improvement, show t…
University of Toronto（多伦多大学）；Michigan State University（密歇根州立大学）
Reinforcement learning (RL) is a powerful data-driven control method that has been largely explored in autonomous driving tasks. However, conventional RL approaches learn control policies through trial-and-error interactions with the environment and therefore may cause disastrous consequences such as collisions when testing in real-world traffic. Offline RL has recently emerged as a promising framework to learn effective policies from previously-collected, static datasets without the requirement of active interactions, making it especially appealing for autonomous driving applications. Despite…
Off-Policy Safe Reinforcement Learning with Constrained Optimistic Exploration
Faculty of Mechanical Engineering（机械工程学院）；Delft University of Technology（代尔夫特理工大学）；Faculty of Electrical Engineering, Mathematics and Computer Science（电气工程、数学和计算机科学学院）
University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）；Cornell University（康奈尔大学）；Microsoft Corporation（微软公司）
Reinforcement Learning (RL) and continuous nonlinear control have been successfully deployed in multiple domains of complicated sequential decision-making tasks. However, given the exploration nature of the learning process and the presence of model uncertainty, it is challenging to apply them to safety-critical control tasks due to the lack of safety guarantee. On the other hand, while combining control-theoretical approaches with learning algorithms has shown promise in safe RL applications, the sample efficiency of safe data collection process for control is not well addressed. In this pape…
In Interactive Machine Learning (IML), we iteratively make decisions and obtain noisy observations of an unknown function. While IML methods, e.g., Bayesian optimization and active learning, have been successful in applications, on real-world systems they must provably avoid unsafe decisions. To this end, safe IML algorithms must carefully learn about a priori unknown constraints without making unsafe decisions. Existing algorithms for this problem learn about the safety of all decisions to ensure convergence. This is sample-inefficient, as it explores decisions that are not relevant for the o…
Platform-Agnostic Reinforcement Learning Framework for Safe Exploration of Cluttered Environments with Graph Attention
Robotics and AI Group, Department of Computer Science, Electrical and Space Engineering, Luleå University of Technology（机器人与人工智能组，计算机科学、电气与空间工程系，吕勒奥技术大学）
Aalto University（阿尔托大学）；Örebro University（厄勒布鲁大学）；KTH Royal Institute of Technology（KTH皇家理工学院）
Policy search reinforcement learning allows robots to acquire skills by themselves. However, the learning procedure is inherently unsafe as the robot has no a-priori way to predict the consequences of the exploratory actions it takes. Therefore, exploration can lead to collisions with the potential to harm the robot and/or the environment. In this work we address the safety aspect by constraining the exploration to happen in safe-to-explore state spaces. These are formed by decomposing target skills (e.g., grasping) into higher ranked sub-tasks (e.g., collision avoidance, joint limit avoidance…
