基于灰色定性方法的主观不确定性知识表达与路径规划算法研究
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摘要
由于客观环境的复杂性或智能系统认知能力的限制,智能系统从环境中获取的知识往往具有不确定性。模拟人类智能对不确定性知识进行表达和处理并形式化地表示不确定性知识,使机器具有不确定性智能,是人工智能领域的研究热点之一。在对环境的认知过程中,人类往往是从环境中逐步获得知识并选择性地记忆重要环境信息,这使得根源于知识不完备性的主观不确定性知识成为人类记忆中不确定性知识的主要类型之一。目前,移动机器人逐渐步入人类的日常生活,需要能够和人类进行交互,需要以类似于人类智能的模式来表达环境知识并完成导航任务,移动机器人具备表达并应用主观不确定性知识能力的需求日益迫切。因此主观不确定性知识的表达以及基于主观不确定性知识的推理、决策等理论和方法的研究对于移动机器人智能性的提高有着重要的意义。
灰色系统理论致力于研究主观不确定性知识的表达,而定性理论中建立的系统建模、问题分析等方法侧重于人类智能特点的模拟,本文融合灰色系统理论和定性理论的特点,建立主观不确定性知识的灰色定性表达方法,目标是形成一套符合人类智能思维模式的知识表达体系,并在此基础上建立定性定量集成的智能推理和决策方法。再以灰色定性知识表达方法为基础,分析人类认知地图特点,构造综合人类认知地图与机器人导航地图优势的灰色定性地图,建立基于灰色定性地图的机器人路径规划算法。实验表明,在环境知识的复杂度、路径规划效果方面本文方法均有一定优势。
本文的主要工作和贡献如下：
(1)融合灰色系统理论和定性理论的特点,以灰色定性基本元、灰色定性基本元的关键点集,灰色定性量空间、灰色定性关系、灰色定性特征值以及广义白化函数为核心概念建立主观不确定性知识灰色定性表达方法体系。灰色定性基本元、灰色定性量空间、灰色定性关系分别对应定性理论中本体基元、量空间、因果性三个基本要素；灰色定性基本元、灰色定性基本元的关键点集和广义白化函数分别对应于灰色系统理论中的区间灰数、区间灰数的边界点和白化函数。以灰色定性基本元作为融合灰色系统理论和定性理论的桥梁。
(2)指出客观不确定性系统和主观不确定性系统的区别,提出一种针对仅有少量已知主观不确定性规则的系统的灰色定性建模方法,模拟人类智能在未知环境中不断积累、融合以及应用主观不确定性规则的能力。
(3)综合国内外对认知地图的现有研究成果以及灰色定性知识表达方法,提出既适合于人机交互又适合于机器人导航需求的灰色定性地图：以环境的剖分及剖分之间的邻接关系作为定性层,模拟人类智能的认知地图,便于人机交互；以剖分的顶点坐标及势场向量为定量信息,用于决定机器人在导航过程中的运动速率及方向。灰色定性地图的特点还在于其模拟了人类智能记忆环境知识的特点,可以用环境中少量关键信息支持机器人完成路径规划任务,降低了环境模型的复杂度。
(4)提出一种基于灰色定性地图的无陷阱人工势场算法,利用灰色定性地图中剖分的顶点坐标及势场向量计算整个环境中的势场,解决了因仅用障碍物斥力和目标点吸引力计算的传统人工势场中存在陷阱而使目标点不可达的问题。再进一步对此算法进行了优化,通过调整灰色定性基本元的部分顶点坐标及势场向量,使得机器人可以在基于灰色定性地图的人工势场中获得平滑路径,便于实际应用。
Due to the complexity of the objective environment or the cognitive ability limit of the intelligent systems, the knowledge gained from the environment by the intelligent systems is uncertain. The research on how to simulate human intelligence to represent and process the uncertain knowledge and represent it formally, endowing the robot the ability to process uncertain knowledge, is one of the hot spot in AI. During the perception process for environment, human always gather environment knowledge step by step and select the most important information for storing. This fact makes the subjective uncertain knowledge which stems from the incompleteness of knowledge become one of the most important uncertain knowledge in human memory. At present, mobile robot gradually step into the daily life of human beings. So it needs the ability to interact with human, the ability to represent and use the subjective uncertain knowledge which similar to human intelligence. As a result, research on theory and methods of how to represent subjective uncertain knowledge and the corresponding reasoning, decision methods have an important significance for improvement of mobile intelligence.
Grey system theory is aimed at represent subjective knowledge. On the other hand, the methods of system modeling and problem analysis method in qualitative theory show the interest in imitating human intelligence. Aiming at establishing a knowledge representation method that complies with human intelligence, and then establishing a method which is both qualitative and quantitative to achieve intelligent reasoning and decision based on the knowledge representation system, the paper proposes a new method-grey qualitative knowledge representation method to represent subjective uncertain knowledge which makes a fusion of grey system theory and qualitative theory. And then, based on the proposed knowledge representation method and the features of human cognitive map, grey qualitative map which combine the superiorities of both cognitive map and navigation map is proposed. The path planning algorithm based on grey qualitative map is also proposed. The experiments results show the advantages in both knowledge complexity and path planning result.
The main contributions are as follows:
(1) We developed the grey qualitative representation method for representing subjective uncertain knowledge by integrating the features of the grey system theory and the qualitative theory. The method is composed of grey qualitative fundamental element, the set of key points of grey qualitative fundamental element, grey qualitative fundamental element space, grey qualitative relationship, grey qualitative characteristic values and generalized whitening function. Grey qualitative element, grey qualitative fundamental element space and grey qualitative relationship are respectively correspond to ontology primitive, quantity space and causality which are all basic elements in qualitative theory. The grey qualitative fundamental element, the set of key points of grey qualitative fundamental element and the generalized whitening function are correspond to interval grey number, the boundary points of interval grey number and whitening function in grey system theory respectively. We use grey qualitative element as the bridge for the integration of grey system theory and qualitative theory.
(2) Show the difference between objective uncertain system and subjective uncertain system. Grey qualitative modeling method is proposed for modeling systems with a small amount of known subjective uncertain rules. The proposed method simulates human intelligence in gathering, fusion and using subjective uncertain knowledge in unknown environment.
(3) By investigating the existing research on the cognitive map at home and abroad and the grey qualitative knowledge representation method, a grey qualitative map is proposed which suitable for both mobile robot navigation and inaction with human. We define the environment subdivisions and adjacent relationship between then as a qualitative layer of the map, which is used for simulating cognitive map of human intelligence. The quantitative layer including coordinates of vertices of subdivisions and the vector of potential field are used for deciding the robot speed and direction in the navigation process. Another superiority of grey qualitative map is that it can support robot complete path planning task based on a little of key information of environment, which reduce the complexity of environment model.
(4) An artificial potential field without traps algorithm based on grey qualitative map is proposed. By calculating the potential field with the key message in grey qualitative map, we solve the local trap problem exists in the traditional artificial potential field which calculated only by repulsive force of obstales and attractive force of target. And further, by adjusting part of vertex coordinates of grey qualitative elements and the potential field vector, the algorithm is optimized. By this, the robot can obtain a smooth path in artificial potential field, which facilitating the practical application.
灰色系统理论致力于研究主观不确定性知识的表达,而定性理论中建立的系统建模、问题分析等方法侧重于人类智能特点的模拟,本文融合灰色系统理论和定性理论的特点,建立主观不确定性知识的灰色定性表达方法,目标是形成一套符合人类智能思维模式的知识表达体系,并在此基础上建立定性定量集成的智能推理和决策方法。再以灰色定性知识表达方法为基础,分析人类认知地图特点,构造综合人类认知地图与机器人导航地图优势的灰色定性地图,建立基于灰色定性地图的机器人路径规划算法。实验表明,在环境知识的复杂度、路径规划效果方面本文方法均有一定优势。
本文的主要工作和贡献如下：
(1)融合灰色系统理论和定性理论的特点,以灰色定性基本元、灰色定性基本元的关键点集,灰色定性量空间、灰色定性关系、灰色定性特征值以及广义白化函数为核心概念建立主观不确定性知识灰色定性表达方法体系。灰色定性基本元、灰色定性量空间、灰色定性关系分别对应定性理论中本体基元、量空间、因果性三个基本要素；灰色定性基本元、灰色定性基本元的关键点集和广义白化函数分别对应于灰色系统理论中的区间灰数、区间灰数的边界点和白化函数。以灰色定性基本元作为融合灰色系统理论和定性理论的桥梁。
(2)指出客观不确定性系统和主观不确定性系统的区别,提出一种针对仅有少量已知主观不确定性规则的系统的灰色定性建模方法,模拟人类智能在未知环境中不断积累、融合以及应用主观不确定性规则的能力。
(3)综合国内外对认知地图的现有研究成果以及灰色定性知识表达方法,提出既适合于人机交互又适合于机器人导航需求的灰色定性地图：以环境的剖分及剖分之间的邻接关系作为定性层,模拟人类智能的认知地图,便于人机交互；以剖分的顶点坐标及势场向量为定量信息,用于决定机器人在导航过程中的运动速率及方向。灰色定性地图的特点还在于其模拟了人类智能记忆环境知识的特点,可以用环境中少量关键信息支持机器人完成路径规划任务,降低了环境模型的复杂度。
(4)提出一种基于灰色定性地图的无陷阱人工势场算法,利用灰色定性地图中剖分的顶点坐标及势场向量计算整个环境中的势场,解决了因仅用障碍物斥力和目标点吸引力计算的传统人工势场中存在陷阱而使目标点不可达的问题。再进一步对此算法进行了优化,通过调整灰色定性基本元的部分顶点坐标及势场向量,使得机器人可以在基于灰色定性地图的人工势场中获得平滑路径,便于实际应用。
Due to the complexity of the objective environment or the cognitive ability limit of the intelligent systems, the knowledge gained from the environment by the intelligent systems is uncertain. The research on how to simulate human intelligence to represent and process the uncertain knowledge and represent it formally, endowing the robot the ability to process uncertain knowledge, is one of the hot spot in AI. During the perception process for environment, human always gather environment knowledge step by step and select the most important information for storing. This fact makes the subjective uncertain knowledge which stems from the incompleteness of knowledge become one of the most important uncertain knowledge in human memory. At present, mobile robot gradually step into the daily life of human beings. So it needs the ability to interact with human, the ability to represent and use the subjective uncertain knowledge which similar to human intelligence. As a result, research on theory and methods of how to represent subjective uncertain knowledge and the corresponding reasoning, decision methods have an important significance for improvement of mobile intelligence.
Grey system theory is aimed at represent subjective knowledge. On the other hand, the methods of system modeling and problem analysis method in qualitative theory show the interest in imitating human intelligence. Aiming at establishing a knowledge representation method that complies with human intelligence, and then establishing a method which is both qualitative and quantitative to achieve intelligent reasoning and decision based on the knowledge representation system, the paper proposes a new method-grey qualitative knowledge representation method to represent subjective uncertain knowledge which makes a fusion of grey system theory and qualitative theory. And then, based on the proposed knowledge representation method and the features of human cognitive map, grey qualitative map which combine the superiorities of both cognitive map and navigation map is proposed. The path planning algorithm based on grey qualitative map is also proposed. The experiments results show the advantages in both knowledge complexity and path planning result.
The main contributions are as follows:
(1) We developed the grey qualitative representation method for representing subjective uncertain knowledge by integrating the features of the grey system theory and the qualitative theory. The method is composed of grey qualitative fundamental element, the set of key points of grey qualitative fundamental element, grey qualitative fundamental element space, grey qualitative relationship, grey qualitative characteristic values and generalized whitening function. Grey qualitative element, grey qualitative fundamental element space and grey qualitative relationship are respectively correspond to ontology primitive, quantity space and causality which are all basic elements in qualitative theory. The grey qualitative fundamental element, the set of key points of grey qualitative fundamental element and the generalized whitening function are correspond to interval grey number, the boundary points of interval grey number and whitening function in grey system theory respectively. We use grey qualitative element as the bridge for the integration of grey system theory and qualitative theory.
(2) Show the difference between objective uncertain system and subjective uncertain system. Grey qualitative modeling method is proposed for modeling systems with a small amount of known subjective uncertain rules. The proposed method simulates human intelligence in gathering, fusion and using subjective uncertain knowledge in unknown environment.
(3) By investigating the existing research on the cognitive map at home and abroad and the grey qualitative knowledge representation method, a grey qualitative map is proposed which suitable for both mobile robot navigation and inaction with human. We define the environment subdivisions and adjacent relationship between then as a qualitative layer of the map, which is used for simulating cognitive map of human intelligence. The quantitative layer including coordinates of vertices of subdivisions and the vector of potential field are used for deciding the robot speed and direction in the navigation process. Another superiority of grey qualitative map is that it can support robot complete path planning task based on a little of key information of environment, which reduce the complexity of environment model.
(4) An artificial potential field without traps algorithm based on grey qualitative map is proposed. By calculating the potential field with the key message in grey qualitative map, we solve the local trap problem exists in the traditional artificial potential field which calculated only by repulsive force of obstales and attractive force of target. And further, by adjusting part of vertex coordinates of grey qualitative elements and the potential field vector, the algorithm is optimized. By this, the robot can obtain a smooth path in artificial potential field, which facilitating the practical application.
引文
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