Sampling-based motion planning with temporal goals

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.

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.

In this paper we describe the problem of motion planning for mul- tiple goals in unstructured environments by using temporal logic for speci- cation of the goals. We solve the problem of mission planning for mobile robots, wherein the goal of the robot can be a complex mission speci cation rather than a classical "Go from A to B" problem. To achieve this problem we take a two dimensional map of the real environment and identify the re- gions of interest, navigable areas and non-navigable areas, which are tagged to make the nal map. We also assume that during the motion of the robot the current position is known and the environment is stationary. We describe the high level planing algorithm which gives a trajectory catering to the tem- poral logic based goal speci cation. We use optimal graph search to search for an optimal solution, while at each step checking for the validity of the temporal logic. Simulation results to various practical scenarios are provided making a robot act over high level speci cations while yielding optimal plans.

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.

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.

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 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.

2015 IEEE International Conference on Robotics and Automation (ICRA), 2015

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.

2011

Abstract This article describes approach for solving motion planning problems for mobile robots involving temporal goals. Traditional motion planning for mobile robotic systems involves the construction of a motion plan that takes the system from an initial state to a set of goal states while avoiding collisions with obstacles at all times. The motion plan is also required to respect the dynamics of the system that are typically described by a set of differential equations.

2019 International Conference on Robotics and Automation (ICRA), 2019

This work addresses the problem of robot navigation under timed temporal specifications in workspaces cluttered with obstacles. We propose a hybrid control strategy that guarantees the accomplishment of a high-level specification expressed as a timed temporal logic formula, while preserving safety (i.e., obstacle avoidance) of the system. In particular, we utilize a motion controller that achieves safe navigation inside the workspace in predetermined time, thus allowing us to abstract the motion of the agent as a finite timed transition system among certain regions of interest. Next, we employ standard formal verification and convex optimization techniques to derive high-level timed plans that satisfy the agent's specifications. A simulation study illustrates and clarifies the proposed scheme.