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Motion Planning and Trajectory Based Controller Synthesis for Optimal and Correct System Behaviors

机译：基于运动规划和轨迹的控制器综合，可实现最佳和正确的系统行为

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摘要

This dissertation is primarily focused on synthesizing control and motion plan that guarantee correct system behaviors while optimizing a performance objective. In the approaches presented here, the correct system behaviors are defined in terms of safety/reachability specifications and temporal logic specifications. Safety/reachability specifications involve requiring the system to avoid a set of unsafe states at all times and reach a set of goal states within a specific amount of time. Temporal logic specifications extend these system behaviors to more complex specifications such as the system is required to visit different sets of states in a specific order and at specific times.;To solve the safety/reachability control problems we propose to use the concept of trajectory robustness that provides a robust neighborhood around any nominal trajectory of the system satisfying the given safety/reachability specification. If the system is initialized within the robust neighborhood of the nominal trajectory, we can apply the same control input as the nominal trajectory and the resulting system trajectory is guaranteed to always stay within the robust tube defined by that nominal trajectory and its neighborhood. As a result, the new trajectory also satisfies the safety/reachability specifications.;We then develop a motion planner based on Mixed-Integer Linear Programming (MILP) approach such that given a system whose dynamics can be represented with linear equations and desired system specifications in terms of Metric Temporal Logic (MTL) formula or simpler reach-avoid specifications, the motion planner finds a system trajectory that satisfies the specifications, even in dynamically changing environments. In this work, the end goal is to be able to find such trajectories in real-time such that if the environment of the system is changing dynamically in the run-time, the system can still satisfy its desired task specifications given by the MTL formula.;To account for any general nonlinear systems, we also propose a gradient-search based optimization algorithm for motion planning to satisfy MTL specifications. Both the MILP method and this one are capable of minimizing (maximizing) a desired performance criteria. We showcase the usefulness of these approaches in real-world applications, by solving a task and motion planning problem for a manipulator arm for an object rearrangement task. We use a hierarchical framework, where at the high-level the MILP method is used to find proper sequences of movement of the manipulator arm. At the low-level the gradient-based method finds the actual control inputs to realize the arm movement sequence.;Finally, we extend the MILP motion planning approach from a single-agent system to a multi-agent system, where multiple individual agents need to cooperate to realize a group MTL task. We solve this problem by proposing a semi-decentralized approach, where each agent solves its own MILP problem locally, in parallel to all other agents. This leads to a speed-up in the execution time for finding the individual trajectories for each agent, so that the motion planning approach can be implemented in real-time, in a dynamically changing environment.
机译：本文主要致力于控制和运动计划的综合，以保证正确的系统行为，同时优化性能目标。在此处介绍的方法中，根据安全性/可到达性规范和时间逻辑规范定义了正确的系统行为。安全/可达性规范涉及要求系统始终避免一组不安全状态，并在特定时间内达到一组目标状态。时间逻辑规范将这些系统行为扩展到更复杂的规范，例如要求系统按特定顺序在特定时间访问不同的状态集；为解决安全/可达性控制问题，我们建议使用轨迹鲁棒性的概念可以在满足给定安全性/可到达性规范的系统的任何标称轨迹周围提供稳健的邻域。如果系统是在标称轨迹的鲁棒性邻域内初始化的，则我们可以应用与标称轨迹相同的控制输入，并且所得到的系统轨迹将始终保持在该标称轨迹及其邻域所定义的鲁棒管内。结果，新的轨迹也满足了安全性/可达性规范。然后，我们基于混合整数线性规划（MILP）方法开发了运动计划器，使得给定的系统可以用线性方程式和所需的系统规范表示动态根据度量时态逻辑（MTL）公式或更简单的避免触及规格，即使在动态变化的环境中，运动计划者也能找到满足规格的系统轨迹。在这项工作中，最终目标是能够实时找到这样的轨迹，使得如果系统的环境在运行时动态变化，则系统仍可以满足MTL公式给出的所需任务规范为了解决任何一般的非线性系统，我们还提出了一种基于梯度搜索的运动规划优化算法，以满足MTL规范。 MILP方法和该方法都能够最小化（最大化）所需的性能标准。通过解决对象重排任务的机械手的任务和运动计划问题，我们展示了这些方法在实际应用中的实用性。我们使用层次结构的框架，其中在高层使用MILP方法来查找机械臂的正确运动序列。在低层，基于梯度的方法找到实际的控制输入以实现手臂运动序列。最后，我们将MILP运动计划方法从单主体系统扩展到需要多个个体主体的多主体系统。合作实现小组MTL任务。我们通过提出一种半分散的方法来解决此问题，其中每个代理与所有其他代理并行地在本地解决自己的MILP问题。这样可以加快执行时间，以找到每个代理的个体轨迹，从而可以在动态变化的环境中实时实施运动计划方法。

著录项

  • 作者

    Saha, Sayan.;

  • 作者单位

    Rensselaer Polytechnic Institute.;

  • 授予单位 Rensselaer Polytechnic Institute.;
  • 学科 Electrical engineering.;Engineering.
  • 学位 Ph.D.
  • 年度 2017
  • 页码 225 p.
  • 总页数 225
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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