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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. 

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. 

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.