Iterative temporal motion planning for hybrid systems in partially unknown environments (original) (raw)
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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.
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.
Hybrid Controllers for Path Planning: A Temporal Logic Approach
Proceedings of the 44th IEEE Conference on Decision and Control, 2005
Robot motion planning algorithms have focused on low-level reachability goals taking into account robot kinematics, or on high level task planning while ignoring low-level dynamics. In this paper, we present an integrated approach to the design of closed-loop hybrid controllers that guarantee by construction that the resulting continuous robot trajectories satisfy sophisticated specifications expressed in the so-called Linear Temporal Logic. In addition, our framework ensures that the temporal logic specification is satisfied even in the presence of an adversary that may instantaneously reposition the robot within the environment a finite number of times. This is achieved by obtaining a Büchi automaton realization of the temporal logic specification, which supervises a finite family of continuous feedback controllers, ensuring consistency between the discrete plan and the continuous execution.
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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.
Motion planning with complex goals
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.
A motion planner for a hybrid robotic system with kinodynamic constraints
2007
Abstract The rapidly increasing complexity of tasks robotic systems are expected to carry out underscores the need for the development of motion planners that can take into account discrete changes in the continuous motions of the system. Completion of tasks such as exploration of unknown or hazardous environments often requires discrete changes in the controls and motions of the robot in order to adapt to different terrains or maintain operability during partial failures or other mishaps.
Vehicle Motion Planning with Time-Varying Constraints
Journal of Guidance, Control, and Dynamics, 2004
With the growing emphasis on vehicle autonomy, the problem of planning a trajectory in an environment with obstacles has become increasingly important. This task has been of particular interest to roboticists and computer scientists, whose primary focus is on kinematic motion planning . Typical kinematic planning methods fall into two main categories, roadmap methods and incremental search methods, both of which find collision-free paths in the state space. Roadmap methods generate and traverse a graph of collision-free connecting paths spanning the state space, while incremental search methods, including dynamic programming [2] and potential field methods [3], perform an iterative search to connect the initial and goal states. For the purely geometric path planning problem, deterministic algorithms have been created that are complete, i.e., they will find a solution if and only if one exists. Unfortunately, these suffer from high computational costs which are exponential in system degrees of freedom. This cost has motivated the development of iterative randomized path planning algorithms that are probabilistically complete, i.e., if a feasible path exists, the probability of finding a path from the initial to final conditions converges to one as the number of iterations goes to infinity. The introduction of the Rapidly-exploring Random Trees (RRTs) of LaValle and Kuffner [4] allowed both for computationally efficient exploration of a complicated space as well as incorporation of system dynamics. The RRT grows a tree of feasible trajectories from the initial condition, or root node. Each node, or waypoint, on the tree represents a system state and has possible trajectories branching from it. Through use of an embedded planning routine, the tree incrementally builds itself in random direc-Associate Fellow AIAA 1 of 12 tions, node by node, until the final conditions are met (within accuracy bounds). Frazzoli demonstrated that a hybrid systems representation of vehicle dynamics, when coupled with the RRT, could be used to address moving obstacles and time-invariant final conditions in a real-time environment. This paper presents a similar approach which provides probabilistic completeness in the presence of both time-varying obstacles and final conditions while using a simpler algorithmic procedure. In addition, a novel approach to provide error mitigation of the embedded planner in a hybrid system-based RRT is presented. An example is then given in which the proposed algorithm is applied to the landing of a spacecraft on an idealized asteroid.
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...
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.