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 SMT-based algorithm with two carefully crafted greedy algorithms. Our experimental results show that the proposed algorithm can deal with the dynamism in the workspace in LTL path planning effectively.
This technical report is an extended version of the paper 'A Receding Horizon Algorithm for Informative Path Planning with Temporal Logic Constraints' accepted to the 2013 IEEE International Conference on Robotics and Automation (ICRA). This paper considers the problem of finding the most informative path for a sensing robot under temporal logic constraints, a richer set of constraints than have previously been considered in information gathering. An algorithm for informative path planning is presented that leverages tools from information theory and formal control synthesis, and is proven to …
A*-based Temporal Logic Path Planning with User Preferences on Relaxed Task Satisfaction
Mechanical Engineering and Mechanics Department at Lehigh University（莱维大学机械工程与力学系）；School of Manufacturing Systems and Networks at Arizona State University（亚利桑那州立大学制造系统与网络学院）
TU Berlin（柏林工业大学）；Technion（以色列理工学院）；IBM Research（IBM研究院）
Robotic planning in real-world scenarios typically requires joint optimization of logic and continuous variables. A core challenge to combine the strengths of logic planners and continuous solvers is the design of an efficient interface that informs the logical search about continuous infeasibilities. In this paper we present a novel iterative algorithm that connects logic planning with nonlinear optimization through a bidirectional interface, achieved by the detection of minimal subsets of nonlinear constraints that are infeasible. The algorithm continuously builds a database of graphs that r…
NetApp India（NetApp印度公司）；Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）；SAP India（SAP印度公司）
Motion planning is the core problem to solve for developing any application involving an autonomous mobile robot. The fundamental motion planning problem involves generating a trajectory for a robot for point-to-point navigation while avoiding obstacles. Heuristic-based search algorithms like A* have been shown to be extremely efficient in solving such planning problems. Recently, there has been an increased interest in specifying complex motion plans using temporal logic. In the state-of-the-art algorithm, the temporal logic motion planning problem is reduced to a graph search problem and Dij…
This paper addresses a multi-robot planning problem in environments with partially unknown semantics. The environment is assumed to have known geometric structure (e.g., walls) and to be occupied by static labeled landmarks with uncertain positions and classes. This modeling approach gives rise to an uncertain semantic map generated by semantic SLAM algorithms. Our goal is to design control policies for robots equipped with noisy perception systems so that they can accomplish collaborative tasks captured by global temporal logic specifications. To specify missions that account for environmenta…
In this paper, we propose a sampling-based motion planning algorithm that finds an infinite path satisfying a Linear Temporal Logic (LTL) formula over a set of properties satisfied by some regions in a given environment. The algorithm has three main features. First, it is incremental, in the sense that the procedure for finding a satisfying path at each iteration scales only with the number of new samples generated at that iteration. Second, the underlying graph is sparse, which guarantees the low complexity of the overall method. Third, it is probabilistically complete. Examples illustrating …
Korea Advanced Institute of Science and Technology（韩国科学技术院）
We present a task-and-motion planning (TAMP) algorithm robust against a human operator's cooperative or adversarial interventions. Interventions often invalidate the current plan and require replanning on the fly. Replanning can be computationally expensive and often interrupts seamless task execution. We introduce a dynamically reconfigurable planning methodology with behavior tree-based control strategies toward reactive TAMP, which takes the advantage of previous plans and incremental graph search during temporal logic-based reactive synthesis. Our algorithm also shows efficient recovery fu…
Institute of Industrial and Control Engineering (IOC), Universitat Politècnica de Catalunya (UPC) – Barcelona Tech（加泰罗尼亚理工大学工业与控制工程研究所）
One of the main foci of robotics is nowadays centered in providing a great degree of autonomy to robots. A fundamental step in this direction is to give them the ability to plan in discrete and continuous spaces to find the required motions to complete a complex task. In this line, some recent approaches describe tasks with Linear Temporal Logic (LTL) and reason on discrete actions to guide sampling-based motion planning, with the aim of finding dynamically-feasible motions that satisfy the temporal-logic task specifications. The present paper proposes an LTL planning approach enhanced with th…
TU Berlin（柏林工业大学）；International Max Planck Research School for Intelligent Systems（马克斯·普朗克智能系统国际研究学院）；Bilkent University（比尔肯特大学）
Sequential decision-making and motion planning for robotic manipulation induce combinatorial complexity. For long-horizon tasks, especially when the environment comprises many objects that can be interacted with, planning efficiency becomes even more important. To plan such long-horizon tasks, we present the RHH-LGP algorithm for combined task and motion planning (TAMP). First, we propose a TAMP approach (based on Logic-Geometric Programming) that effectively uses geometry-based heuristics for solving long-horizon manipulation tasks. The efficiency of this planner is then further improved by a…
University Stuttgart（斯图加特大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Logic-Geometric Programming (LGP) is a powerful motion and manipulation planning framework, which represents hierarchical structure using logic rules that describe discrete aspects of problems, e.g., touch, grasp, hit, or push, and solves the resulting smooth trajectory optimization. The expressive power of logic allows LGP for handling complex, large-scale sequential manipulation and tool-use planning problems. In this paper, we extend the LGP formulation to stochastic domains. Based on the control-inference duality, we interpret LGP in a stochastic domain as fitting a mixture of Gaussians to…
Our goal in this paper is to plan the motion of a robot in a partitioned environment with dynamically changing, locally sensed rewards. We assume that arbitrary assumptions on the reward dynamics can be given. The robot aims to accomplish a high-level temporal logic surveillance mission and to locally optimize the collection of the rewards in the visited regions. These two objectives often conflict and only a compromise between them can be reached. We address this issue by taking into consideration a user-defined preference function that captures the trade-off between the importance of collect…
Replanning in temporal logic tasks is extremely difficult during the online execution of robots. This study introduces an effective path planner that computes solutions for temporal logic goals and instantly adapts to non-static and partially unknown environments. Given prior knowledge and a task specification, the planner first identifies an initial feasible solution by growing a sampling-based search tree. While carrying out the computed plan, the robot maintains a solution library to continuously enhance the unfinished part of the plan and store backup plans. The planner updates existing pl…
Boston University（波士顿大学）；University of Waterloo（滑铁卢大学）；Massachusetts Institute of Technology（麻省理工学院）
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 re…
Lexicographic Minimum-Violation Motion Planning using Signal Temporal Logic
School of Computation, Information and Technology, Technical University of Munich（慕尼黑技术大学计算信息与技术学院）；ZF Friedrichshafen AG（弗赖堡汽车集团）；Institute of System Dynamics, HTWG Konstanz（康斯坦茨HTWG系统动力学研究所）
Boston University（波士顿大学）；University of Waterloo（滑铁卢大学）；United Technologies Research Center（联合技术研究中心）
In this paper we present a method for automatically planning robust 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, and the mission is given as a Linear Temporal Logic (LTL) formula over a set of propositions satisfied by the regions of the environment. In addition, an optimizing proposition must repeatedly be satisfied. The goal is to minimize the maximum time between satisfying instances of the optimizing proposition while ensuring that the LTL formula is satisfied e…
Optimization-based Task and Motion Planning under Signal Temporal Logic Specifications using Logic Network Flow
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology（佐治亚理工学院机械工程学院）；Georgia Institute of Technology（佐治亚理工学院）；School of Electrical and Computer Engineering, Georgia Institute of Technology（佐治亚理工学院电气与计算机工程学院）
SAP Labs, India（思爱普实验室（印度））；IIT Kanpur, India（印度坎普尔理工学院）
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 automata-theoretic model checking technique to solve this problem. This approach involves computation of a product graph of the Buchi 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 algo…
Towards Tighter Convex Relaxation of Mixed-Integer Programs: Leveraging Logic Network Flow for Task and Motion Planning
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, USA（乔治亚理工学院机械工程学院）；Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, USA（乔治亚理工学院工业与系统工程学院）
Bridging Perception and Planning: Towards End-to-End Planning for Signal Temporal Logic Tasks
School of Automation & Intelligent Sensing, Shanghai Jiao Tong University（自动化与智能感知学院，上海交通大学）；University of Minnesota, Twin Cities（明尼苏达大学，双城分校）；School of Information Science and Technology, University of Science and Technology of China（信息科学与技术学院，中国科学技术大学）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Massachusetts Institute of Technology（麻省理工学院）
We tackle the challenging problem of multi-agent cooperative motion planning for complex tasks described using signal temporal logic (STL), where robots can have nonlinear and nonholonomic dynamics. Existing methods in multi-agent motion planning, especially those based on discrete abstractions and model predictive control (MPC), suffer from limited scalability with respect to the complexity of the task, the size of the workspace, and the planning horizon. We present a method based on {\em timed waypoints\/} to address this issue. We show that timed waypoints can help abstract nonlinear behavi…
For a nonlinear system (e.g. a robot) with its continuous state space trajectories constrained by a linear temporal logic specification, the synthesis of a low-level controller for mission execution often results in a non-convex optimization problem. We devise a new algorithm to solve this type of non-convex problems by formulating a rapidly-exploring random tree of barrier pairs, with each barrier pair composed of a quadratic barrier function and a full state feedback controller. The proposed method employs a rapid-exploring random tree to deal with the non-convex constraints and uses barrier…
KTH Royal Institute of Technology（KTH皇家理工学院）；School of Electrical Engineering and Computer Science（电气工程与计算机科学学院）
Control and planning of multi-agent systems is an active and increasingly studied topic of research, with many practical applications such as rescue missions, security, surveillance, and transportation. This thesis addresses the planning and control of multi-agent systems under temporal logic tasks. The considered systems concern complex, robotic, manipulator-endowed systems, which can coordinate in order to execute complicated tasks, including object manipulation/transportation. Motivated by real-life scenarios, we take into account high-order dynamics subject to model uncertainties and unkno…
University of Science and Technology of China（中国科学技术大学）；Lehigh University（利哈伊大学）；University of Iowa（爱荷华大学）
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 pre-specified timed missions cannot be fully satisfied. Such issues become even more challenging when considering ti…
Signal Temporal Logic Motion Planning via Graphs of Convex Sets
School of Automation & Intelligent Sensing, Shanghai Jiao Tong University（自动化与智能感知学院，上海交通大学）；Institute of Artificial Intelligence, Xiamen University（人工智能研究院，厦门大学）
DAG-STL: A Hierarchical Framework for Zero-Shot Trajectory Planning under Signal Temporal Logic Specifications
School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China（自动化与智能感知学院，上海交通大学，上海，中国）；Institute of Artificial Intelligence, Xiamen University, Xiamen, China（人工智能研究院，厦门大学，厦门，中国）
This article presents an approach to encode Linear Temporal Logic (LTL) Specifications into a Mixed Integer Quadratically Constrained Quadratic Program (MIQCQP) footstep planner. We propose that the integration of LTL specifications into the planner not only facilitates safe and desirable locomotion between obstacle-free regions, but also provides a rich language for high-level reasoning in contact planning. Simulations of the footstep planner in a 2D environment satisfying encoded LTL specifications demonstrate the results of this research.
This paper proposes a new reactive temporal logic planning algorithm for multiple robots that operate in environments with unknown geometry modeled using occupancy grid maps. The robots are equipped with individual sensors that allow them to continuously learn a grid map of the unknown environment using existing Simultaneous Localization and Mapping (SLAM) methods. The goal of the robots is to accomplish complex collaborative tasks, captured by global Linear Temporal Logic (LTL) formulas. The majority of existing LTL planning approaches rely on discrete abstractions of the robot dynamics opera…
This paper investigates the task coordination of multi-robot where each robot has a private individual temporal logic task specification; and also has to jointly satisfy a globally given collaborative temporal logic task specification. To efficiently generate feasible and optimized task execution plans for the robots, we propose a hierarchical multi-robot temporal task planning framework, in which a central server allocates the collaborative tasks to the robots, and then individual robots can independently synthesize their task execution plans in a decentralized manner. Furthermore, we propose…
Instituto Balseiro - Universidad Nacional de Cuyo（巴尔塞罗研究所 - 库约国立大学）；CNEA（阿根廷国家原子能委员会）；Universidad de Buenos Aires（布宜诺斯艾利斯大学）；Imperial College London（帝国理工学院）
Temporal logic task planning for robotic systems suffers from state explosion when specifications involve large numbers of discrete locations. We provide a novel approach, particularly suited for tasks specifications with universally quantified locations, that has constant time with respect to the number of locations, enabling synthesis of plans for an arbitrary number of them. We propose a hybrid control framework that uses an iterator to manage the discretised workspace hiding it from a plan enacted by a discrete event controller. A downside of our approach is that it incurs in increased ove…
