Sampling-based motion planning with temporal goals (original) (raw)

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.

Motion planning with temporal-logic specifications: Progress and challenges

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.

Temporal Logic based Motion Planning in Unstructured Environments

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.

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.

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.

MT* : Multi-Robot Path Planning for Temporal Logic Specifications

ArXiv, 2021

We address the path planning problem for a team of robots satisfying a complex high-level mission specification given in the form of an Linear Temporal Logic (LTL) formula. The state-of-the-art approach to this problem employs the automatatheoretic model checking technique to solve this problem. This approach involves computation of a product graph of the Büchi automaton generated from the LTL specification and a joint transition system which captures the collective motion of the robots and then computation of the shortest path using Dijkstra’s shortest path algorithm. We propose MT*, an algorithm that reduces the computation burden for generating such plans for multi-robot systems significantly. Our approach generates a reduced version of the product graph without computing the complete joint transition system, which is computationally expensive. It then divides the complete mission specification among the participating robots and generates the trajectories for the individual robot...

CTP: A new constraint-based formalism for conditional, temporal planning

Temporal constraints pose a challenge for conditional planning, because it is necessary for a conditional planner to determine whether a candidate plan will satisfy the specified temporal constraints. This can be difficult, because temporal assignments that satisfy the constraints associated with one conditional branch may fail to satisfy the constraints along a different branch. In this paper we address this challenge by developing the Conditional Temporal Problem (CTP) formalism, an extension of standard temporal constraint-satisfaction processing models used in non-conditional temporal planning. Specifically, we augment temporal CSP frameworks by (1) adding observation nodes, and (2) attaching labels to all nodes to indicate the situation(s) in which each will be executed. Our extended framework allows for the construction of conditional plans that are guaranteed to satisfy complex temporal constraints. Importantly, this can be achieved even while allowing for decisions about the precise timing of actions to be postponed until execution time, thereby adding flexibility and making it possible to dynamically adapt the plan in response to the observations made during execution. We also show that, even for plans without explicit quantitative temporal constraints, our approach fixes a problem in the earlier approaches to conditional planning, which resulted in their being incomplete.

Optimal temporal logic planning with cascading soft constraints

2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2019

In this paper, we address the problem of temporal logic planning given both hard specifications of the robot's mission and soft preferences on the plans that achieve the mission. In particular, we consider a problem whose inputs are a transition system, a linear temporal logic (LTL) formula specifying the robot's mission, and an ordered sequence of formulas expressed in linear dynamic logic over finite traces (LDL f) specifying the user's preferences for how the mission should be completed. The planner's objective is to synthesize, on this transition system, an infinite trajectory that best fits the user's preferences over finite prefixes of that trajectory while nonetheless satisfying the overall objective. We describe an algorithm for this problem that constructs, from the inputs, a product automaton-which is, in fact, a special kind of stateweighted Büchi automaton-over which an optimal trajectory is synthesized. This synthesis problem is solved via reduction to the minimax path problem in vertex weighted graphs, which can be solved by variants of the standard algorithms for computing shortest paths in a graph or by algorithms for the all-pairs bottleneck paths problem on vertex-weighted graphs. We show the applicability of the approach via some case studies, for which we present results computed by an implementation.

Optimal multi-robot path planning with temporal logic constraints

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2011

In this paper we present a method for automatically planning optimal paths for a group of robots that satisfy a common high level mission specification. Each robot's motion in the environment is modeled as a weighted transition system. The mission is given as a Linear Temporal Logic formula. In addition, an optimizing proposition must repeatedly be satisfied. The goal is to minimize the maximum time between satisfying instances of the optimizing proposition. Our method is guaranteed to compute an optimal set of robot paths. We utilize a timed automaton representation in order to capture the relative position of the robots in the environment. We then obtain a bisimulation of this timed automaton as a finite transition system that captures the joint behavior of the robots and apply our earlier algorithm for the single robot case to optimize the group motion. We present a simulation of a persistent monitoring task in a road network environment.

A Flexible Sampling-Based Approach to Task and Motion Planning

2019

Generalized robot autonomy requires robots to plan solutions for complex and varied tasks involving interaction with the physical world. Traditionally, the (continuous) geometric and (discrete) symbolic aspects of the problem are studied independently; motion planners solve geometric problems, whereas task planners solve symbolic problems. Integrated Task and Motion Planning (TAMP) seeks to unify the planning problem using information from each component to ease the solution of the other. Most TAMP approaches focus on information flow between task and motion planners; the majority of these approaches integrate the motion planning layer into the task planning layer as a source of constraints and/or a validator for task plans [1, 2, 5, 8]. Validating task plans with a motion planner may require repeated expensive executions of both planners. Getting constraints from the motion planner is more efficient but is often limited by the manual selection of a restricted subset of motion const...