The Heuristic of Directional Qualitative Semantic: A New Heuristic for Making Decisions about Spinning with Qualitative Reasoning
2. The Research Program: Multifunctional Robot on Topological Notions
- A table with the agent’s actions labeled by one of the three following relations: . The meaning of the labels depends on the kind of the reference system that represents the position of the space. For example, if it is egocentric, < means that the action causes the values of the objects to increase after it is applied, = means that the action does not cause a change in the values of the objects after it is applied, and > means that the action causes the values of the objects to decrease after it is applied.
- A set of rules to assign the corresponding TRLG to each agent and object.
- A TRLG is selected according to the size of the objects and .
- The relative topological relation between the objects and is calculated from their current positions, , and the number associated with the node of in the TRLG, , is stored.
- The number, , associated with the node of the relative topological relation that is the target between the objects and , , is obtained.
- It is checked which order relation holds between and from the following:The definitions of the relations must agree with the labeling of actions.
- It is examined at the means-ends table using the order relation that holds between and in order to select the action that is labeled with the same order relation. This is the action selected by heuristics.
3. Qualitative Reasoning about Orientation and Spinning
- A is a region of the Euclidean space .
- The environment has only two objects: a motionless object and an agent.
- The agent has two actions: spinning left and right.
3.1. Initial Assumptions
- The two-dimensional space has a Euclidean geometry. This geometry describes the physical space of our daily life.
- The agent is symmetrical, and its rotating point is the center of mass, considering the agent would have its mass distributed uniformly. This assumption is assumed because most robots have a symmetric shape, and even humans and many other animals are symmetric.
- If the object is concave, it is not surrounding the agent fully or partially. This is assumed because if an object is surrounding the agent, the concept of the direction of the object has lost its meaning and we cannot assign a direction. Therefore, the agent cannot be inside one of the cavities of another object. Because an agent in a cavity is surrounded by the object, we cannot discuss directional relation between the agent and the object. Figure 3 gives two examples of situations in which direction does and does not make sense. Instead, an agent surrounded by an object should be represented through a topological relation, as discussed in a previous article .
- The agent cannot collide with the object while spinning. It implies that the shortest distance from the object to the agent’s rotation point is greater than the distance from the farthest point from the agent to its rotation point.
3.2. Transforming Directional Information into Topological Information
- An agent with continuous symmetry does not modify the agent’s spatial position when it spins.
- Spinning actions modify the direction between an agent and an object, even if the agent has a continuous symmetry.
|Algorithm 1 Algorithm to calculate the Directional Topological Relation (DTR).|
|Ensure: Directional Topological Relation.|
3.3. Heuristic of Directional Qualitative Semantic
|Algorithm 2 Heuristic of Directional Qualitative Semantic (HDQS).|
|Ensure: A sequence of actions to establish a DTR.|
3.4. Selecting a Directional Topological Reasoning Graph
- , , or determine .
- determines .
- , , or determine .
- If the positional variant is + or ≈, and the relative topological relation is Disjoint-0, Meet-0, or Overlap-0, the visual system spins to the left.
- If the positional variant is + or ≈, and the relative topological relation is Overlap-1, Meet-1, or Disjoint-1, the visual system spins to the right.
- If the positional variant is −, and the relative topological relation is Disjoint-0, Meet-0, or Overlap-0, the visual system spins to the right.
- If the positional variant is +, and the relative topological relation is Overlap-1, Meet-1, or Disjoint-1, the visual system spins to the left.
- If the positional variant is +, ≈, or −, and the relative topological relation is Disjoint-0, Meet-0, or Overlap-0, the visual system spins to the left.
- If the positional variant is +, ≈, or −, and the relative topological relation is Overlap-1, Meet-1, or Disjoint-1, the visual system spins to the right.
|Algorithm 3 Algorithm to select a Directional Topological Reasoning Graph (DTRG).|
|Ensure:Directional Topological Reasoning Graph.|
5. Applying the HDQS
- Detect the lateral doors to the left and right of the agent.
- Include establishing a horizontal orientation to a lateral door as the goal to achieve in the Base of Qualitative Goals.
- Include the case without horizontal doors in the inference motor.
- Decide between using the HTQS or HDQS in accordance with the kind of goal.
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
|CTTC||Cognitive Theory of True Conditions|
|RTR||Relative Topological Relation|
|DTR||Directional Topological Relation|
|DTRG||Directional Topological Reasoning Graph|
|HTQS||Heuristic of Topological Qualitative Semantic|
|HDQS||Heuristic of Directional Qualitative Semantic|
|MROTN||Multifunctional Robot On Topological Notions|
|TQNA||Topological Qualitative Navigation Architecture|
|TRLG||Topological Reasoning Lineal Graph|
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|Case||Subcase||Id||Topological Reasoning Lineal Graph|
|Id||Directional Topological Reasoning Graph|
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Miguel-Tomé, S. The Heuristic of Directional Qualitative Semantic: A New Heuristic for Making Decisions about Spinning with Qualitative Reasoning. Robotics 2021, 10, 17. https://doi.org/10.3390/robotics10010017
Miguel-Tomé S. The Heuristic of Directional Qualitative Semantic: A New Heuristic for Making Decisions about Spinning with Qualitative Reasoning. Robotics. 2021; 10(1):17. https://doi.org/10.3390/robotics10010017Chicago/Turabian Style
Miguel-Tomé, Sergio. 2021. "The Heuristic of Directional Qualitative Semantic: A New Heuristic for Making Decisions about Spinning with Qualitative Reasoning" Robotics 10, no. 1: 17. https://doi.org/10.3390/robotics10010017