Analogical reasoning has been implemented in agents to use information about past experiences to guide future action. A similar process for analogical reasoning would enable a robot to reuse past experiences, such as the tasks that an interactive robot could learn from a human teacher. However, in a robotics domain, analogical reasoning must be performed over the knowledge obtained from sensor input and must result in actionable output in the form of the robot's joint configurations. Thus, robotics provides a challenging domain for analogical reasoning, as abstraction plays a necessary role in representing the robot's task knowledge. We explore the problem of abstraction for a robot which performs analogical reasoning, and provide an example task illustrating how abstraction is necessary for a robot to reason over learned tasks.
In the context of an agent which learns to execute tasks, analogical reasoning
can be used to transfer known task knowledge from a source task to address an
unfamiliar, target problem. A similar process can be applied to a robotic agent,
where the problem the robot seeks to address is a task environment observed in
the real-world, and the task plan the robot executes consists of a series of motor
commands. After observing a new target problem, the robot would identify a
relevant task plan from memory, using a method such as that described in [
By implementing an analogical reasoning approach to task transfer, a robot could reuse task knowledge in a wider range of target problems. However, a challenge of applying analogical reasoning to the robotics domain is that it must operate over knowledge represented at a low-level of abstraction. This problem makes it dicult to identify high-level analogs between a source and target problem, such as similar relationships between the robot’s actions and the objects it observes, and then use this analogy to address the target problem. We introduce the challenges of applying analogical reasoning in a robotic agent, and describe preliminary results demonstrating how the level of abstraction at which task knowledge is represented a↵ ects how it can be transferred. 2
We focus on the problem of enabling analogical reasoning for a robot which learns to complete real-world tasks on a tabletop workspace, such as pouring a cup or stacking a set of blocks. We assume that the robot is taught the task by a human teacher who moves the robot’s arm through the action of completing the task. This results in a representation of the task containing two forms of input: – A point-cloud representation of the observed scene, consisting of px,y = <r, g, b, d> containing the color (in RGB format) and depth of each x, y coordinate in the observed frame. – A joint-space trajectory recorded during the task demonstration, containing a set of joint configurations dt = <j0, j1, ..., jn> where jn is the position of a single joint in the robot’s arm at the timestamp t.
Both the source and target environments are perceived via the overhead
camera. However, while an action is learned for the source task, the robot does
not yet have an action model which can be executed to achieve the task in
the target environment. This representation occurs at a low-level of abstraction
because it does not present any relation between the task goal, the observed
objects, and/or the demonstrated action. Thus, the analogs between a source and
target problem are not initially apparent, and it becomes essential to abstract
the task representation at some level in order to perform analogical reasoning.
3
We approach the problem of analogical reasoning in a robotic domain as one
of correctly abstracting a task demonstration for each reasoning problem. When
the robot receives a demonstration of the task, it is stored in memory in the
representation S =< D, T, O, F > where:
– D is the set of sub-skill models recorded during the demonstration, where
D =< d0, ..., dn > and n is the number of sub-skills comprising the task.
Each subskill di is represented as a Dynamic Movement Primitive (DMP)
that is trained from the task demonstration as defined by [
We derive several abstractions of this representation, as listed in Table 1. In
the first abstraction, most of the demonstration representation is retained, with
the exclusion of low-level features (such as object locations and orientation) that
are specific to the environment in which the task was learned. The second
representation further abstracts the task by removing object labels, thus removing
the assumption that all instances of the task will contain the same objects. A
result of this abstraction is that the robot must additionally be provided with
a mapping between objects in the source and target environments before it can
execute the task using this representation. We currently provide this mapping
manually; however, in future work, we intend to have the robot predict this
object mapping by further interacting with the human teacher. In [
The third abstraction is the highest-level representation, in which only the sub-skill models are retained. By excluding the object relations element of the demonstrated task, which dictates the relation between the robot’s hand and each object during the task, the task constraints which were present in the demonstration are no longer enforced. Thus, a new set of task constraints must be introduced so that the task plan can be executed accordingly. We currently Demonstration Sub-skills, Object Relations, Object Labels, Object Features Abstraction 1 Sub-skills, Object Relations, Object Labels Abstraction 2 Sub-skills, Object Relations Abstraction 3 Sub-skills
Table 1: Features Present at Each Level of Similarity (a) Source Environment (b) Displaced
Objects (c) Replaced
Objects (d) Replaced Scoop provide these updated constraints manually, with future work addressing the problem of inferring task constraints. Additionally, as in the second abstraction, an object mapping is necessary before the task can be executed. 4
We evaluated the impact of abstraction on variations of a scooping task, shown in Figure 1, in which the target environment di↵ered from the source environment in one of three ways: (i) object displacement, in which all objects were retained but moved to di↵erent locations, (ii) object replacement, where new objects were introduced and displaced, and (iii) scoop replacement, which altered the constraints of the task since the robot now needed to keep its hand at a di↵erent height to account for the change in scoop length. 4.1
Preliminary Results After providing a single demonstration of the scooping task to the robot learner, we counted the number of successful task executions performed by the robot in each of ten di↵erent target environments when using each of the three abstraction levels. These results are recorded in Table 2. The task could be executed consistently in the displaced-objects environments using any of the three abstractions, since these target environments were most similar to the source environment.
However, in problems where the target environment was more dissimilar from the source environment, an abstracted representation was necessary to correctly execute the task. The replaced-objects environments could only be addressed consistently when the task was represented at the second or third levels of abstraction, and the replaced-scoop environments could only be addressed using the third, most-abstracted representation. These results suggest that as the source and target environment become more dissimilar, abstraction is necessary in order to correctly address the target task. 5
Task transfer becomes a more nuanced problem when the agent’s input and output occurs in the domain of low-level perception and action, because the task must first be abstracted using a higher-level representation. The described experiment and preliminary results support the claim that there is a correlation between (i) the level of similarity between the source and target environments and (ii) the level of abstraction that should be used to address a transfer problem. This indicates that di↵erent transfer problems may require that knowledge is represented at di↵erent levels of abstraction.
In future work, we plan to address the problem of detecting the level of similarity between the source and target environments. Once a level of similarity has been determined for a particular transfer problem, the appropriate level of abstraction for transfer can be selected.
Acknowledgments. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE1148903.