Hybrid Controllers for Path Planning: A Temporal Logic Approach (original) (raw)
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Temporal logic motion planning for dynamic robots
Automatica, 2009
In this paper, we address the temporal logic motion planning problem for mobile robots that are modeled by second order dynamics. Temporal logic specifications can capture the usual control specifications such as reachability and invariance as well as more complex specifications like sequencing and obstacle avoidance. Our approach consists of three basic steps. First, we design a control law that enables the dynamic model to track a simpler kinematic model with a globally bounded error. Second, we built a robust temporal logic specification that takes into account the tracking errors of the first step. Finally, we solve the new robust temporal logic path planning problem for the kinematic model using automata theory and simple local vector fields. The resulting continuous time trajectory is provably guaranteed to satisfy the initial user specification.
Temporal Logic Motion Planning for Mobile Robots
2006
In this paper, we consider the problem of robot motion planning in order to satisfy formulas expressible in temporal logics. Temporal logics naturally express traditional robot specifications such as reaching a goal or avoiding an obstacle, but also more sophisticated specifications such as sequencing, coverage, or temporal ordering of different tasks. In order to provide computational solutions to this problem, we first construct discrete abstractions of robot motion based on some environmental decomposition. We then generate discrete plans satisfying the temporal logic formula using powerful model checking tools, and finally translate the discrete plans to continuous trajectories using hybrid control. Critical to our approach is providing formal guarantees ensuring that if the discrete plan satisfies the temporal logic formula, then the continuous motion also satisfies the exact same formula.
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AI Communications, 2015
Integrating task and motion planning is becoming increasingly important due to the recognition that a growing number of robotics applications in navigation, search-and-rescue missions, manipulation, and medicine involve reasoning with both discrete abstractions and continuous motions. The problem poses unique computational challenges: a vast hybrid discrete/continuous space must be searched while accounting for complex geometries, motion dynamics, collision avoidance, and temporal goals. This paper takes the position that continued progress relies on integrative approaches that bring together techniques from robotics and AI. In this context, the paper examines robot motion planning with temporal-logic specifications and discusses open challenges and directions for future research. The paper aims to promote a continuing dialog between robotics and AI communities.
Where's Waldo? Sensor-Based Temporal Logic Motion Planning
Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007
Given a robot model and a class of admissible environments, this paper provides a framework for automatically and verifiably composing controllers that satisfy high level task specifications expressed in suitable temporal logics. The desired task specifications can express complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, resulting in a novel paradigm for sensor-based temporal logic motion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multi-robot specifications. Our computational approach is based on first creating discrete controllers satisfying so-called General Reactivity(1) formulas. If feasible, the discrete controller is then used in order to guide the sensor-based composition of continuous controllers resulting in a hybrid controller satisfying the high level specification, but only if the environment is admissible.
Temporal-Logic-Based Reactive Mission and Motion Planning
IEEE Transactions on Robotics, 2000
This paper provides a framework to automatically generate a hybrid controller that guarantees that the robot can achieve its task when a robot model, a class of admissible environments, and a high-level task or behavior for the robot are provided. The desired task specifications, which are expressed in a fragment of linear temporal logic (LTL), can capture complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, which results in a novel paradigm for sensor-based temporal-logicmotion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multirobot specifications in a decentralized manner. Our computational approach is based on first creating discrete controllers satisfying specific LTL formulas. If feasible, the discrete controller is then used to guide the sensor-based composition of continuous controllers, which results in a hybrid controller satisfying the highlevel specification but only if the environment is admissible.
Online Motion Planning with Soft Timed Temporal Logic in Dynamic and Unknown Environment
ArXiv, 2021
Motion planning of an autonomous system with high-level specifications has wide applications. However, research of formal languages involving timed temporal logic is still under investigation. Furthermore, many existing results rely on a key assumption that user-specified tasks are feasible in the given environment. Challenges arise when the operating environment is dynamic and unknown since the environment can be found prohibitive, leading to potentially conflicting tasks where prespecified LTL tasks cannot be fully satisfied. Such issues become even more challenging when considering timed requirements. To address these challenges, this work proposes a control framework that considers hard constraints to enforce safety requirements and soft constraints to enable task relaxation. The metric interval temporal logic (MITL) specifications are employed to deal with time constraints. By constructing a relaxed timed product automaton, an online motion planning strategy is synthesized with...
DT*: Temporal Logic Path Planning in a Dynamic Environment
ArXiv, 2021
Path planning for a robot is one of the major problems in the area of robotics. When a robot is given a task in the form of a Linear Temporal Logic (LTL) specification such that the task needs to be carried out repetitively, we want the robot to follow the shortest cyclic path so that the number of times the robot completes the mission within a given duration gets maximized. In this paper, we address the LTL path planning problem in a dynamic environment where the newly arrived dynamic obstacles may invalidate some of the available paths at any arbitrary point in time. We present DT*, an SMT-based receding horizon planning strategy that solves an optimization problem repetitively based on the current status of the workspace to lead the robot to follow the best available path in the current situation. We implement our algorithm using the Z3 SMT solver and evaluate it extensively on an LTL specification capturing a pick-and-drop application in a warehouse environment. We compare our S...
Proceedings of the AAAI Conference on Artificial Intelligence
The specification of complex motion goals through temporal logics is increasingly favored in robotics to narrow the gap between task and motion planning. A major limiting factor of such logics, however, is their Boolean satisfaction condition. To relax this limitation, we introduce a method for quantifying the satisfaction of co-safe linear temporal logic specifications, and propose a planner that uses this method to synthesize robot trajectories with the optimal satisfaction value. The method assigns costs to violations of specifications from user-defined proposition costs. These violation costs define a distance to satisfaction and can be computed algorithmically using a weighted automaton. The planner utilizes this automaton and an abstraction of the robotic system to construct a product graph that captures all possible robot trajectories and their distances to satisfaction. Then, a plan with the minimum distance to satisfaction is generated by employing this graph as the high-le...
Automatic Trajectory Synthesis for Real-Time Temporal Logic
IEEE Transactions on Automatic Control, 2022
Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from temporal logic specifications. Existing approaches, however, have been limited to relatively short and simple specifications. Furthermore, existing methods either consider some prior discretization of the state-space, deal only with a convex fragment of temporal logic, or are not provably complete. We propose a scalable, provably complete algorithm that synthesizes continuous trajectories to satisfy non-convex Temporal Logic over Reals (RTL) specifications. We separate discrete task planning and continuous motion planning on-the-fly and harness highly efficient boolean satisfiability (SAT) and Linear Programming (LP) solvers to find dynamically feasible trajectories that satisfy non-convex RTL specifications for high dimensional systems. The proposed design algorithms are proven sound and complete, and simulation results demonstrate our approach's scalability.
Motion planning with hybrid dynamics and temporal goals
2010
Abstract In this paper, we consider the problem of motion planning for mobile robots with nonlinear hybrid dynamics, and high-level temporal goals. We use a multi-layered synergistic framework that has been proposed recently for solving planning problems involving hybrid systems and high-level temporal goals. In that framework, a high-level planner employs a user-defined discrete abstraction of the hybrid system as well as exploration information to suggest high-level plans.