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We investigate the synthesis of optimal controllers for continuous-time and continuous-state systems under temporal logic specifications. The specification is expressed as a deterministic, finite automaton (the specification automaton) with transition costs, and the optimal system behavior is captured by a cost function that is integrated over time. We construct a dynamic programming problem over...
This paper describes the implementation of an interface connecting the two tools : the JPL SCA (Statechart Autocoder) and TuLiP (Temporal Logic Planning Toolbox) to enable the automatic synthesis of low level implementation code directly from formal specifications. With system dynamics, bounds on uncertainty and formal specifications as inputs, TuLiP synthesizes Mealy machines that are correct-by-construction...
Temporal logics have proven effective for correct-by-construction synthesis of controllers for a wide range of robotic applications. Receding horizon frameworks mitigate the computational intractability of reactive synthesis for temporal logic, but have thus far been limited by pursuing a single sequence of short horizon problems to the goal. We propose a receding horizon algorithm for reactive synthesis...
We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that...
Augmented finite transition systems generalize nondeterministic transition systems with additional liveness conditions. We propose efficient algorithms for synthesizing control protocols for augmented finite transition systems to satisfy high-level specifications expressed in a fragment of linear temporal logic (LTL). We then use these algorithms within a framework for switching protocol synthesis...
We present a method for mending strategies for GR(1) specifications. Given the addition or removal of edges from the game graph describing a problem (essentially transition rules in a GR(1) specification), we apply a μ-calculus formula to a neighborhood of states to obtain a “local strategy” that navigates around the invalidated parts of an original synthesized strategy. Our method may thus avoid...
The cost of the great expressivity of motion planning subject to temporal logic formulae is intractability. Recent advances in sampling-based methods seem to be only applicable to “low-level” control. The problem of realizing “high-level” controllers that satisfy a temporal logic specification does not readily admit approximations, unless the notion of correctness is relaxed as might be achieved with...
We present a method for designing a robust control policy for an uncertain system subject to temporal logic specifications. The system is modeled as a finite Markov Decision Process (MDP) whose transition probabilities are not exactly known but are known to belong to a given uncertainty set. A robust control policy is generated for the MDP that maximizes the worst-case probability of satisfying the...
In robotic finger gaiting, fingers continuously manipulate an object until joint limitations or mechanical limitations periodically force a switch of grasp. Current approaches to gait planning and control are slow, lack formal guarantees on correctness, and are generally not reactive to changes in object geometry. To address these issues, we apply advances in formal methods to model a gait subject...
This paper considers the problem of synthesizing correct-by-construction robotic controllers in environments with uncertain but fixed structure. “Environment” has two notions in this work: a map or “world” in which some controlled agent must operate and navigate (i.e., evolve in a configuration space with obstacles); and an adversarial player that selects continuous and discrete variables to try to...
We present a methodology for automatic synthesis of embedded control software that incorporates a class of linear temporal logic (LTL) specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. To alleviate the associated computational complexity of LTL synthesis, we propose a receding horizon framework that effectively...
We considered the problem of designing control protocols for pan-tilt-zoom (PTZ) cameras within a smart camera network where the goal is to guarantee certain temporal logic specifications related to a given surveillance task. We first present a centralized control architecture for assigning PTZ cameras to targets so that the specification is met for any admissible behavior of the targets. Then, in...
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