Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions

A multi-agent partially observable Markov decision process (MPOMDP) is a modeling paradigm used for high-level planning of heterogeneous autonomous agents subject to uncertainty and partial observation. Despite their modeling efficiency, MPOMDPs have not received significant attention in safety-critical settings. In this paper, we use barrier functions to design policies for MPOMDPs that ensure safety. Notably, our method does not rely on discretization of the belief space, or finite memory. To this end, we formulate sufficient and necessary conditions for the safety of a given set based on discrete-time barrier functions (DTBFs) and we demonstrate that our formulation also allows for Boolean compositions of DTBFs for representing more complicated safe sets. We show that the proposed method can be implemented online by a sequence of one-step greedy algorithms as a standalone safe controller or as a safety-filter given a nominal planning policy. We illustrate the efficiency of the proposed methodology based on DTBFs using a high-fidelity simulation of heterogeneous robots.Comment: 8 pages and 4 figure

Barrier Functions for Multiagent-POMDPs with DTL Specifications

Multi-agent partially observable Markov decision processes (MPOMDPs) provide a framework to represent heterogeneous autonomous agents subject to uncertainty and partial observation. In this paper, given a nominal policy provided by a human operator or a conventional planning method, we propose a technique based on barrier functions to design a minimally interfering safety-shield ensuring satisfaction of high-level specifications in terms of linear distribution temporal logic (LDTL). To this end, we use sufficient and necessary conditions for the invariance of a given set based on discrete-time barrier functions (DTBFs) and formulate sufficient conditions for finite time DTBF to study finite time convergence to a set. We then show that different LDTL mission/safety specifications can be cast as a set of invariance or finite time reachability problems. We demonstrate that the proposed method for safety-shield synthesis can be implemented online by a sequence of one-step greedy algorithms. We demonstrate the efficacy of the proposed method using experiments involving a team of robots

Automated Formation Control Synthesis from Temporal Logic Specifications

In this paper, we propose a novel framework using formal methods to synthesize a navigation control strategy for a multi-robot swarm system with automated formation. The main objective of the problem is to navigate the robot swarm toward a goal position while passing a series of waypoints. The formation of the robot swarm should be changed according to the terrain restrictions around the corresponding waypoint. Also, the motion of the robots should always satisfy certain runtime safety requirements, such as avoiding collision with other robots and obstacles. We prescribe the desired waypoints and formation for the robot swarm using a temporal logic (TL) specification. Then, we formulate the transition of the waypoints and the formation as a deterministic finite transition system (DFTS) and synthesize a control strategy subject to the TL specification. Meanwhile, the runtime safety requirements are encoded using control barrier functions, and fixed-time control Lyapunov functions ensure fixed-time convergence. A quadratic program (QP) problem is solved to refine the DFTS control strategy to generate the control inputs for the robots, such that both TL specifications and runtime safety requirements are satisfied simultaneously. This work enlights a novel solution for multi-robot systems with complicated task specifications. The efficacy of the proposed framework is validated with a simulation study

Verification of Uncertain POMDPs Using Barrier Certificates

We consider a class of partially observable Markov decision processes (POMDPs) with uncertain transition and/or observation probabilities. The uncertainty takes the form of probability intervals. Such uncertain POMDPs can be used, for example, to model autonomous agents with sensors with limited accuracy, or agents undergoing a sudden component failure, or structural damage [1]. Given an uncertain POMDP representation of the autonomous agent, our goal is to propose a method for checking whether the system will satisfy an optimal performance, while not violating a safety requirement (e.g. fuel level, velocity, and etc.). To this end, we cast the POMDP problem into a switched system scenario. We then take advantage of this switched system characterization and propose a method based on barrier certificates for optimality and/or safety verification. We then show that the verification task can be carried out computationally by sum-of-squares programming. We illustrate the efficacy of our method by applying it to a Mars rover exploration example.Comment: 8 pages, 4 figure

Model-based Dynamic Shielding for Safe and Efficient Multi-Agent Reinforcement Learning

Multi-Agent Reinforcement Learning (MARL) discovers policies that maximize reward but do not have safety guarantees during the learning and deployment phases. Although shielding with Linear Temporal Logic (LTL) is a promising formal method to ensure safety in single-agent Reinforcement Learning (RL), it results in conservative behaviors when scaling to multi-agent scenarios. Additionally, it poses computational challenges for synthesizing shields in complex multi-agent environments. This work introduces Model-based Dynamic Shielding (MBDS) to support MARL algorithm design. Our algorithm synthesizes distributive shields, which are reactive systems running in parallel with each MARL agent, to monitor and rectify unsafe behaviors. The shields can dynamically split, merge, and recompute based on agents' states. This design enables efficient synthesis of shields to monitor agents in complex environments without coordination overheads. We also propose an algorithm to synthesize shields without prior knowledge of the dynamics model. The proposed algorithm obtains an approximate world model by interacting with the environment during the early stage of exploration, making our MBDS enjoy formal safety guarantees with high probability. We demonstrate in simulations that our framework can surpass existing baselines in terms of safety guarantees and learning performance.Comment: Accepted in AAMAS 202

Automated Formation Control Synthesis from Temporal Logic Specifications

In this paper, we propose a novel framework using formal methods to synthesize a navigation control strategy for a multi-robot swarm system with automated formation. The main objective of the problem is to navigate the robot swarm toward a goal position while passing a series of waypoints. The formation of the robot swarm should be changed according to the terrain restrictions around the corresponding waypoint. Also, the motion of the robots should always satisfy certain runtime safety requirements, such as avoiding collision with other robots and obstacles. We prescribe the desired waypoints and formation for the robot swarm using a temporal logic (TL) specification. Then, we formulate the transition of the waypoints and the formation as a deterministic finite transition system (DFTS) and synthesize a control strategy subject to the TL specification. Meanwhile, the runtime safety requirements are encoded using control barrier functions, and fixed-time control Lyapunov functions ensure fixed-time convergence. A quadratic program (QP) problem is solved to refine the DFTS control strategy to generate the control inputs for the robots, such that both TL specifications and runtime safety requirements are satisfied simultaneously. This work enlights a novel solution for multi-robot systems with complicated task specifications. The efficacy of the proposed framework is validated with a simulation study