Safe Control Design Research Articles

Learning safe control for multi-robot systems: Methods, verification, and open challenges

In this survey, we review the recent advances in control design methods for robotic multi-agent systems (MAS), focusing on learning-based methods with safety considerations. We start by reviewing various notions of safety and liveness properties, and modeling frameworks used for problem formulation of MAS. Then we provide a comprehensive review of learning-based methods for safe control design for multi-robot systems. We start with various shielding-based methods, such as safety certificates, predictive filters, and reachability tools. Then, we review the current state of control barrier certificate learning in both a centralized and distributed manner, followed by a comprehensive review of multi-agent reinforcement learning with a particular focus on safety. Next, we discuss the state-of-the-art verification tools for the correctness of learning-based methods. Based on the capabilities and the limitations of the state-of-the-art methods in learning and verification for MAS, we identify various broad themes for open challenges: how to design methods that can achieve good performance along with safety guarantees; how to decompose single-agent-based centralized methods for MAS; how to account for communication-related practical issues; and how to assess transfer of theoretical guarantees to practice.

Rule-Based Safe Probabilistic Movement Primitive Control via Control Barrier Functions

In this paper, we develop a novel and safe control design approach that takes demonstrations provided by a human teacher to enable a robot to accomplish complex manipulation scenarios in dynamic environments. First, an overall task is divided into multiple simpler subtasks that are more appropriate for learning and control objectives. Then, by collecting human demonstrations, the subtasks that require robot movement are modeled by probabilistic movement primitives (ProMPs). We also study two strategies for modifying the ProMPs to avoid collisions with environmental obstacles. Finally, we introduce a rule-base control technique by utilizing a finite-state machine along with a unique means of control design for ProMPs. For the ProMP controller, we propose control barrier and Lyapunov functions to guide the system along a trajectory within the distribution defined by a ProMP while guaranteeing that the system state never leaves more than a desired distance from the distribution mean. This allows for better performance on nonlinear systems and offers solid stability and known bounds on the system state. A series of simulations and experimental studies demonstrate the efficacy of our approach and show that it can run in real time. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the need to create a teach-by-demonstration framework that captures the strengths of movement primitives and verifiable, safe control. We provide a framework that learns safe control laws from a probability distribution of robot trajectories through the use of advanced nonlinear control that incorporates safety constraints. Typically, such distributions are stochastic, making it difficult to offer any guarantees on safe operation. Our approach ensures that the distribution of allowed robot trajectories is within an envelope of safety and allows for robust operation of a robot. Furthermore, using our framework various probability distributions can be combined to represent complex scenarios in the environment. It will benefit practitioners by making it substantially easier to test and deploy accurate, efficient, and safe robots in complex real-world scenarios. The approach is currently limited to scenarios involving static obstacles, with dynamic obstacle avoidance an avenue of future effort.

Safe control synthesis using environmentally robust control barrier functions

In this paper, we study a safe control design for dynamical systems in the presence of uncertainty in a dynamical environment. The worst-case error approach is considered to formulate robust Control Barrier Functions (CBFs) in an optimization-based control synthesis framework. It is first shown that environmentally robust CBF formulations result in second-order cone programs (SOCPs). Then, a novel scheme is presented to formulate robust CBFs which takes the nominally safe control as its desired control input in optimization-based control design and then tries to minimally modify it whenever the robust CBF constraint is violated. This proposed scheme leads to quadratic programs (QPs) which can be easily solved. Finally, the effectiveness of the proposed approach is demonstrated on an adaptive cruise control example.

Minimum-Variance and Low-Complexity Data-Driven Probabilistic Safe Control Design

This paper presents a direct minimum-variance (MV) data-driven safe control design approach for uncertain linear discrete-time stochastic systems. The superiority of the direct MV approach is shown by developing and comparing direct versus indirect learning approaches and MV versus certainty-equivalence (CE) approaches. First, it is shown that probabilistic safety can be guaranteed by ensuring probabilistic λ-contractivity of the safe set. Four data-based convex optimization-based algorithms are introduced to ensure the probabilistic λ-contractivity of the safe set (i.e., direct and indirect CE, direct and indirect MV). It is shown that while the CE approach results in a risk-neutral control design method with no robustness guarantees, the MV approach results in a risk-averse control design with probabilistic safety guarantees. This is because MV approach aims at learning a control gain that minimizes the variance of the state of the closed-loop system with respect to the safe set, and thus minimizes the risk of safety violation. Besides, it is shown that the direct learning approach requires weaker data richness conditions (i.e., lower sample complexity) than the indirect learning approach. Two simulation examples are provided to verify that the direct MV learning approach outperforms the other three approaches since it leads to low-complexity (i.e., low sample complexity and convex optimization) safe learning with a high probability of safety guarantees.

A Multi-Fidelity Bayesian Approach to Safe Controller Design

A Multi-Fidelity Bayesian Approach to Safe Controller Design

Safe Control Design for Unknown Nonlinear Systems with Koopman-based Fixed-Time Identification

We consider the problem of safe control design for a class of nonlinear, control-affine systems subject to an unknown, additive, nonlinear disturbance. Leveraging recent advancements in the application of Koopman operator theory to the field of system identification and control, we introduce a novel fixed-time identification scheme for the infinitesimal generator of the infinite-dimensional, but notably linear, Koopman dynamical system analogous to the nonlinear system of interest. That is, we derive a parameter adaptation law that allows us to recover the unknown, residual nonlinear dynamics in the system within a finite-time, independent of an initial estimate. We then use properties of fixed-time stability to derive an estimation error bound on the unknown dynamics as an explicit function of time, which allows us to synthesize a safe controller using control barrier function based methods. We conduct a quadrotor-inspired case study in support of our proposed method, in which we show that safe trajectory tracking is achieved despite unknown, nonlinear dynamics.

Differentiable Safe Controller Design Through Control Barrier Functions

Learning-based controllers, such as neural network (NN) controllers, can show high empirical performance but lack formal safety guarantees. To address this issue, control barrier functions (CBFs) have been applied as a safety filter to monitor and modify the outputs of learning-based controllers in order to guarantee the safety of the closed-loop system. However, such modification can be myopic with unpredictable long-term effects. In this work, we propose a safe-by-construction NN controller which employs differentiable CBF-based safety layers, and investigate the performance of safe-by-construction NN controllers in learning-based control. Specifically, two formulations of controllers are compared: one is projection-based and the other relies on our proposed set-theoretic parameterization. Both methods demonstrate improved closed-loop performance over using CBF as a separate safety filter in numerical experiments.

Barrier-Certified Learning-Enabled Safe Control Design for Systems Operating in Uncertain Environments

Barrier-Certified Learning-Enabled Safe Control Design for Systems Operating in Uncertain Environments

A Safety-Certified Policy Iteration Algorithm for Control of Constrained Nonlinear Systems

This letter designs safe controllers with guaranteed performance for continuous-time systems under state constraints. While existing safe control frameworks mainly ignore the performance of the controller and existing optimal control frameworks ignore the safety of the controller, the presented approach brings the best of both worlds of safe control design and optimal control design together. To this end, a novel safe policy iteration algorithm is presented that iteratively finds an optimal controller while certifying the safety of the improved control policy at each iteration. To avoid solving a Hamilton-Jacobi Bellman (HJB) equality for finding the optimal control policy, which does not guarantee safety, an HJB inequality is solved that can be integrated with barrier certificate to verify the safety of the control policy. Sum-of-Squares program is employed to implement the presented policy iteration algorithm and thus iteratively find a safe control solution with guaranteed performance. A simulation example is provided to verify the effectiveness of the proposed approach.

Fault-tolerant safe control design of switched and interconnected nonlinear systems

This paper provides novel fault-tolerant safe control (FTSC) strategies for switched and interconnected nonlinear systems. With several switching and interconnection situations considered, the proposed corresponding strategies ensure that the state never enters the unsafe set and asymptotically converges to the origin in the presence of faults. This relies on a proposed concept named “fault-tolerant control Lyapunov-Barrier functions (FTCLBF)”. Two practical examples are taken to demonstrate the efficiency of the proposed method.

On the Application of ISO 26262 in Control Design for Automated Vehicles

Research on automated vehicles has experienced an explosive growth over the past decade. A main obstacle to their practical realization, however, is a convincing safety concept. This question becomes ever more important as more sophisticated algorithms are used and the vehicle automation level increases. The field of functional safety offers a systematic approach to identify possible sources of risk and to improve the safety of a vehicle. It is based on practical experience across the aerospace, process and other industries over multiple decades. This experience is compiled in the functional safety standard for the automotive domain, ISO 26262, which is widely adopted throughout the automotive industry. However, its applicability and relevance for highly automated vehicles is subject to a controversial debate. This paper takes a critical look at the discussion and summarizes the main steps of ISO 26262 for a safe control design for automated vehicles.

Control design pattern based on safety logical constraints for manufacturing systems: application to a palletizer

This paper presents an original approach for safe controller design for manufacturing systems controlled by PLC (Programmable Logic Controller). In this work, manufacturing systems are considered as Discrete Event Systems (DES) with logical Inputs (sensors) and logical Outputs (actuators). The proposed approach, which separates the functional control part from the safety control part, is easy to implement and ensures that the designed controller is safe. The methodology is based on the use of safety constraints in order to get a permissive safe controller which can be validated off line by model-checking. This controller is then constrained by functional constraints. The approach is illustrated with a palletizer simulated process using the ITS PLC software from the Real Games Company (www.realgames.pt). The control algorithm is presented and allows resulting in a safe control using a standard control design pattern, may be simpler than a conventional approach based on a complete specification in GRAFCET (IEC 60848) that does not distinguish the functional aspect from the safety aspect. This approach presents interesting perspectives like the management of several operating modes linked to a Manufacturing Execution System (MES) or the manual modes through Human-Machine Interfaces (HMI) or Supervisory Control and Data Acquisition (SCADA) systems.

QoS Control for Pipelines of Tasks Using Multiple Resources

We consider soft real-time applications organized as pipelines of tasks using resources of different type (communication, computation, and storage). The applications are assumed to be periodically triggered and the different tasks communicate by unidirectional buffers. The problem we cope with is how to effectively share the resources so that some specified Quality of Service (QoS) requirements are met. The QoS considered here is tightly related to the end-to-end temporal behavior of the application. To compensate for time-varying resource requirements, we advocate a distributed control approach whereby the scheduling parameters of each task are tuned depending on the temporal behavior of the application measured by appropriate sensors. The use of real-time scheduling strategies enables a mathematically safe control design in which the QoS requirements are translated into control goals, and formal proofs are provided on the ability of the controller to fulfil these goals. We also offer extensive simulations that validate the approach for multimedia applications.

Methods for Safe Control Systems Design and Implementation

This paper is the introductory one of the Safe control systems session. A classification of methods contributing to control systems safety is proposed in order to place the five other papers of this session and to show that they are complementary. This classification is based on a life-cycle criterion. Focusing then on discrete event systems safety, we point out the relationships between state space synthesis and analysis and system safety. This enables a more formal approach of safe control design and implementation.