Qualitative Representation of Kinematic Robots Honghai Liu and George M. Coghill Department of Computing Science, University of Aberdeen AB24 3UE, Scotland United Kingdom hliu;gcoghill @csd.abdn.ac.uk Abstract This paper proposes a qualitative representation for kinematic robots. First, qualitative geometric primitives are introduced by combining a qualita- tive orientation component and qualitative transla- tion component using normalisation. A position in Cartesian space can be mathematically described by the scalable primitives. Secondly, the qualita- tive positions of the components of a robot are de- rived in terms of qualitative geometry primitives. Thirdly, the representation shows how to connect both quantitative and qualitative representation of the robot. On the one hand, the integration of normalisation and domain theory generates nor- malised labels to introduce the cognitive parame- ters into the proposed representation. On the other hand, the normalized labels of this representation can be converted to a quantitative description us- ing a proposed generator, whose numeric outputs provide a connection to numeric techniques (e.g. interpolation). 1 Introduction There exists an interesting gap between traditional robotics and cognitive robotics, or robot motion and human percep- tion. The reason is two-fold. On the one hand, research in robotics has traditionally emphasized low-level sensing and control tasks including sensor processing, path planning and robot design and control; on the other hand, research in cogni- tive robotics is concerned with endowing robots and software agents with higher level cognitive functions that enable them to reason, act and perceive in changing, incompletely known, and unpredictable environments. This gap is one of crucial is- sues for interdisiplinary research in the engineering commu- nity, robotics community and AI community. It emphasises the goal of robotics research that “robotics is the intelligent connection of perception to action” [Brady, 1985]. Research on qualitative reasoning model-based technol- ogy can be found in [Weld and de Kleer, 1990; Williams and de Kleer, 1991; Faltings and Struss, 1992; Bredeweg and Struss, 2003]. Generally speaking, there are two ap- proaches to qualitative spatial representations [Forbus, 1996; Blackwell, 1988]. One is to explore what aspects do lend themselves to qualitative representation, the other is to use a quantitative representation as a starting point and compute problem-specific qualitative representations to reason with. Cohn and Hazarika [Cohn and Hazarika, 2001] gave suffi- cient overview of qualitative spatial representation and rea- soning techniques by investigating the main aspects of the representation of qualitative knowledge including ontologi- cal aspects, distance, orientation and shape, and qualitative spatial reasoning including reasoning about spatial change. The representation of qualitative kinematics is the best de- veloped field in qualitative spatial representation. Its history can be covered by the following research work. Firstly, The possible motions of objects are represented by qualitative re- gions in configuration space representing the legitimate posi- tions of parts of mechanisms [Faltings, 1992]. Faltings built upon Nielsen and Forbus’ earlier work on qualitative kine- matics [Nielsen, 1988], and developed a first principles algo- rithm for analyzing planar mechanisms. However, this work suffered from the limitation that certain problems could not be solved without including quantitative information. Sec- ondly, Olivier et al proposed a qualitative kinematic reason- ing method based upon the use of occupancy arrays [Olivier et al., 1995]. This approach works simply on the constraint that no two objects occupy the same occupancy array position and can be extended to include semi-quantitative information. Thirdly, Kramer [Kramer, 1992] proposed ’The Linkage As- sistant’ kinematic simulator which demonstrated that mecha- nism kinematic analysis did not solely have to rely on exact geometric mechanism information. Fourthly, Liu [Liu, 1998] presented a qualitative representation and reasoning approach based upon the formalism of qualitative trigonometry, quali- tative arithmetic, and qualitative spatial inference. However, developing a general approach to the representation of qual- itative kinematics is still an open problem. This study aims to develop a general qualitative representation for kinematic robots, the approach also can be extended to general mecha- nisms. The rest of this paper is organized as follows: Section 2 presents qualitative geometric primitives in Cartesian space. Section 3 derives a qualitative representation for qualitative robot kinematics. Section 4 addresses how the representation connect both qualitative states and robot motion. Section 5 concludes this paper.