Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is Linear Temporal Logic (LTL). Policy synthesis on MDPs for properties specified in LTL has been well studied. LTL, however, is defined over infinite traces, while many properties of interest are inherently finite. Linear Temporal Logic over finite traces (LTLf ) has been used to express such properties, but no tools exist to solve policy synthesis for MDP behaviors given finite-trace properties. We present two algorithms for solving this synthesis problem: the first via reduction of LTLf to LTL and the second using native tools for LTLf . We compare the scalability of these two approaches for synthesis and show that the native approach offers better scalability compared to existing automaton generation tools for LTL.
more »
« less
Strategy synthesis for partially-known switched stochastic systems
We present a data-driven framework for strategy synthesis for partially-known switched stochastic systems. The properties of the system are specified using linear temporal logic (LTL) over finite traces (LTLf), which is as expressive as LTL and enables interpretations over finite behaviors. The framework first learns the unknown dynamics via Gaussian process regression. Then, it builds a formal abstraction of the switched system in terms of an uncertain Markov model, namely an Interval Markov Decision Process (IMDP), by accounting for both the stochastic behavior of the system and the uncertainty in the learning step. Then, we synthesize a strategy on the resulting IMDP that maximizes the satisfaction probability of the LTLf specification and is robust against all the uncertainties in the abstraction. This strategy is then refined into a switching strategy for the original stochastic system. We show that this strategy is near-optimal and provide a bound on its distance (error) to the optimal strategy. We experimentally validate our framework on various case studies, including both linear and non-linear switched stochastic systems.
more »
« less
- Award ID(s):
- 2039062
- NSF-PAR ID:
- 10301020
- Date Published:
- Journal Name:
- The 24th International Conference on Hybrid Systems: Computation and Control
- Page Range / eLocation ID:
- 1 to 11
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
LTL synthesis is the problem of synthesizing a reactive system from a formal specification in Linear Temporal Logic. The extension of allowing for partial observability, where the system does not have direct access to all relevant information about the environment, allows generalizing this problem to a wider set of real-world applications, but the difficulty of implementing such an extension in practice means that it has remained in the realm of theory. Recently, it has been demonstrated that restricting LTL synthesis to systems with finite executions by using LTL with finite-horizon semantics (LTLf) allows for significantly simpler implementations in practice. With the conceptual simplicity of LTLf, it becomes possible to explore extensions such as partial observability in practice for the first time. Previous work has analyzed the problem of LTLf synthesis under partial observability theoretically and suggested two possible algorithms, one with 3EXPTIME and another with 2EXPTIME complexity. In this work, we first prove a complexity lower bound conjectured in earlier work. Then, we complement the theoretical analysis by showing how the two algorithms can be integrated in practice into an established framework for LTLf synthesis. We furthermore identify a third, MSO-based, approach enabled by this framework. Our experimental evaluation reveals very different results from what the theory seems to suggest, with the 3EXPTIME algorithm often outperforming the 2EXPTIME approach. Furthermore, as long as it is able to overcome an initial memory bottleneck, the MSO-based approach can often outperforms the others.more » « less
-
Abstract—Often times, we specify tasks for a robot using tem- poral language that can also span different levels of abstraction. The example command “go to the kitchen before going to the second floor” contains spatial abstraction, given that “floor” consists of individual rooms that can also be referred to in isolation (“kitchen”, for example). There is also a temporal ordering of events, defined by the word “before”. Previous works have used Linear Temporal Logic (LTL) to interpret temporal language (such as “before”), and Abstract Markov Decision Processes (AMDPs) to interpret hierarchical abstractions (such as “kitchen” and “second floor”), separately. To handle both types of commands at once, we introduce the Abstract Product Markov Decision Process (AP-MDP), a novel approach capable of representing non-Markovian reward functions at different levels of abstractions. The AP-MDP framework translates LTL into its corresponding automata, creates a product Markov Decision Process (MDP) of the LTL specification and the environment MDP, and decomposes the problem into subproblems to enable efficient planning with abstractions. AP-MDP performs faster than a non-hierarchical method of solving LTL problems in over 95% of tasks, and this number only increases as the size of the en- vironment domain increases. We also present a neural sequence- to-sequence model trained to translate language commands into LTL expression, and a new corpus of non-Markovian language commands spanning different levels of abstraction. We test our framework with the collected language commands on a drone, demonstrating that our approach enables a robot to efficiently solve temporal commands at different levels of abstraction.more » « less
-
null (Ed.)Robots have begun operating and collaborating with humans in industrial and social settings. This collaboration introduces challenges: the robot must plan while taking the human’s actions into account. In prior work, the problem was posed as a 2-player deterministic game, with a limited number of human moves. The limit on human moves is unintuitive, and in many settings determinism is undesirable. In this paper, we present a novel planning method for collaborative human-robot manipulation tasks via probabilistic synthesis. We introduce a probabilistic manipulation domain that captures the interaction by allowing for both robot and human actions with states that represent the configurations of the objects in the workspace. The task is specified using Linear Temporal Logic over finite traces (LTLf ). We then transform our manipulation domain into a Markov Decision Process (MDP) and synthesize an optimal policy to satisfy the specification on this MDP. We present two novel contributions: a formalization of probabilistic manipulation domains allowing us to apply existing techniques and a comparison of different encodings of these domains. Our framework is validated on a physical UR5 robot.more » « less
-
null (Ed.)Linear Temporal Logic (LTL) synthesis aims at automatically synthesizing a program that complies with desired properties expressed in LTL. Unfortunately it has been proved to be too difficult computationally to perform full LTL synthesis. There have been two success stories with LTL synthesis, both having to do with the form of the specification. The first is the GR(1) approach: use safety conditions to determine the possible transitions in a game between the environment and the agent, plus one powerful notion of fairness, Generalized Reactivity(1), or GR(1). The second, inspired by AI planning, is focusing on finite-trace temporal synthesis, with LTLf (LTL on finite traces) as the specification language. In this paper we take these two lines of work and bring them together. We first study the case in which we have an LTLf agent goal and a GR(1) assumption. We then add to the framework safety conditions for both the environment and the agent, obtaining a highly expressive yet still scalable form of LTL synthesis.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3447928.3456649
