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Manipulation planning from high-level task specifications, even though highly desirable, is a challenging problem. The large dimensionality of manipulators and complexity of task specifications make the problem computationally intractable. This work introduces a manipulation planning framework with linear temporal logic (LTL) specifications. The use of LTL as the specification language allows the expression of rich and complex manipulation tasks. The framework deals with the state-explosion problem through a novel abstraction technique. Given a robotic system, a workspace consisting of obstacles, manipulable objects, and locations of interest, and a co-safe LTL specification over the objects and locations, the framework computes a motion plan to achieve the task through a synergistic multi-layered planning architecture. The power of the framework is demonstrated through case studies, in which the planner efficiently computes plans for complex tasks. The case studies also illustrate the ability of the framework in intelligently moving away objects that block desired executions without requiring backtracking.

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Abstract-We present a computational framework for automatic deployment of a robot from a temporal logic specification over a set of properties of interest satisfied at the regions of a partitioned environment. We assume that, during the motion of the robot in the environment, the current region can be precisely determined, while due to sensor and actuation noise, the outcome of a control action can only be predicted probabilistically. Under these assumptions, the deployment problem translates to generating a control strategy for a Markov Decision Process (MDP) from a temporal logic formula. We propose an algorithm inspired from probabilistic Computation Tree Logic (PCTL) model checking to find a control strategy that maximizes the probability of satisfying the specification. We illustrate our method with simulation and experimental results.

Robot control for tasks such as moving around obstacles or grasping objects has advanced significantly in the last few decades. However, controlling robots to perform complex tasks is still accomplished largely by highly trained programmers in a manual, time-consuming, and error-prone process that is typically validated only through extensive testing. Formal methods are mathematical techniques for reasoning about systems, their requirements, and their guarantees. Formal synthesis for robotics refers to frameworks for specifying tasks in a mathematically precise language and automatically transforming these specifications into correct-by-construction robot controllers or into a proof that the task cannot be done. Synthesis allows users to reason about the task specification rather than its implementation, reduces implementation error, and provides behavioral guarantees for the resulting controller. This article reviews the current state of formal synthesis for robotics and surveys the landscape of abstractions, specifications, and synthesis algorithms that enable it.

This paper considers the problem of motion planning for a hybrid robotic system with complex and nonlinear dynamics in a partially unknown environment given a temporal logic specification. We employ a multi-layered synergistic framework that can deal with general robot dynamics and combine it with an iterative planning strategy. Our work allows us to deal with the unknown environmental restrictions only when they are discovered and without the need to repeat the computation that is related to the temporal logic specification. In addition, we define a metric for satisfaction of a specification. We use this metric to plan a trajectory that satisfies the specification as closely as possible in cases in which the discovered constraint in the environment renders the specification unsatisfiable. We demonstrate the efficacy of our framework on a simulation of a hybrid second-order car-like robot moving in an office environment with unknown obstacles. The results show that our framework is successful in generating a trajectory whose satisfaction measure of the specification is optimal. They also show that, when new obstacles are discovered, the reinitialization of our framework is computationally inexpensive.

Stochastic processes are expressive mathematical tools for modeling real-world systems that are subject to uncertainty. It is hence crucial to be able to formally analyze the behavior of these processes, especially in safety-critical applications. Most of the existing formal methods are not designed for continuous-time processes, and those that are typically suffer from state explosion in practice. This work introduces a theoretical framework and a scalable computational method for formal analysis and control synthesis for switched diffusions, a class of stochastic models with linear dynamics that are continuous in both time and space domains; the focus is on safety with possible extensions to other properties. The proposed framework first constructs a finite abstraction in the form of an uncertain Markov process through discretization of both time and space domains. The errors caused by the discretization in each domain are formally characterized and cast into the abstraction model. Then, a strategy that maximizes the probability of the safety property and is robust against the errors is synthesized over the abstraction model. Finally, this robust strategy is mapped to a switching strategy for the stochastic processes that guarantees the safety property. The framework is demonstrated in three case studies, including one that illustrates the trade-off of the error contribution by the time and space discretization parameters.

This work introduces a motion-planning framework for a hybrid system with general continuous dynamics to satisfy a temporal logic specification consisting of co-safety and safety components in a partially unknown environment. The framework employs a multi-layered synergistic planner to generate trajectories that satisfy the specification and adopts an iterative replanning strategy to deal with unknown obstacles. When the discovery of an obstacle renders the specification unsatisfiable, a division between the constraints in the specification is considered. The co-safety component of the specification is treated as a soft constraint, whose partial satisfaction is allowed, while the safety component is viewed as a hard constraint, whose violation is forbidden. To partially satisfy the co-safety component, inspirations