What does learning to ‘draw a circle’ have to do with driving, cycling, unwinding and screwing?
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1
Italian Institute of Technology, Robotics, Brain and Cognitive Science, Italy
Can a baby humanoid learning to draw a circle, at the same time also learn about the abstract notion of ‘Circularity’? Common actions like controlling a steering wheel, uncorking, unwinding, screwing, cycling among others also result in formation of circular movements of different scale, in different coordinate frames, created by different body or tool effectors, causing different environmental consequences, thereby serving different purposes. Similarly, the common denominator in drawing a line, pushing a ball with a stick, pulling an unreachable object closer to oneself with a rake etc is the notion of ‘Straightness’. Undoubtedly, trajectory formation is one of the central functions of the neuromotor controller. Common day to day actions result in formation of spatiotemporal trajectories of different degrees of complexity. Given the diverse range of skilled actions we command effortlessly, it is intriguing to investigate if there is an underlying order/invariance that allows the motor system to systematically ‘compose and reuse’ motor knowledge during the synthesis of purposeful movement. In other words, is there a small set of abstract motor vocabulary that when combined, sequenced, and shaped to ‘context’, allows the emergence of the staggering flexibility, dexterity and range that human actions possess? In this article, we present the design of a hierarchical action generation/learning system for the iCub humanoid that incorporates some crucial properties that could lead to a plausible answer to the above question. We demonstrate the value of the architecture using an example of how motor knowledge acquired by iCub while learning to draw (skill 1) can be systematically recycled in a task of learning to bimanually control a toy crane as a tool to reach otherwise unreachable objects in the environment (skill 2). We believe the underlying mechanism is quite general and can be applied to acquire a wide range of skilled actions in a similar manner. With the help of Figure 1 that shows the central building blocks and high level information flows in our architecture, we outline some crucial/novel features that we believe are fundamental for constructing a growing motor vocabulary in acting/learning robots.
1) Learning through Imitation, Exploration and Motor Imagery: Three streams of learning i.e. learning through teachers demonstration (information flow shown in black arrow), learning through physical interactions (blue arrow) and learning through motor imagery (loop 1-5 shown in black arrow with red outline) are integrated into the architecture. The imitation loop initiates with the teachers demonstration and ends with iCub reproducing the observed action. The motor imagery loop is a sub part of the imitation loop, the only difference being that the motor commands synthesized by the passive motion paradigm [4-5] based forward/inverse model is not transmitted to the actuators. This loop hence allows iCub to internally simulate a range of motor actions and only execute the ones that have high performance score ‘R’. All the three streams are employed while learning the two skills (drawing and crane toy) presented in this article.
2) From Trajectory to ‘Shape, towards ‘Goal Independent’ motor knowledge: Most skilled actions involve synthesis of spatio- temporal trajectories of varying complexity. A crucial feature in our architecture is the introduction of the notion ‘Shape’ in the motor domain. A trajectory may be thought as a sequence of points in space, from a starting position to the ending position. ‘Shape’ is more abstract description of a trajectory, which captures only the essential information or critical events in it. By extracting the ‘shape’ of a trajectory, it is possible make it ‘context independent’ i.e. liberate the trajectory from the details of scale, location, orientation, purpose and body effectors that underlies its creation. Using Catastrophe theory [1], [2] have derived a set of 12 primitive shape critical points (CP) sufficient to describe the shape of any trajectory/line diagram in general. Using this system it is possible to move from visual observation of the end effector trajectory of the teacher to its more abstract ‘shape’ representation. For example, the essence of a trajectory like ‘U’ is the presence of a minima (or Bump ‘B’ critical point) in between two end points (‘E’). Hence the shape is represented as graph ‘E-B-E’. If the ‘U’ was drawn on a paper with a pen or if a boy runs a ‘U’ in a playground, the shape representation does not change. A circle is a composition of 4 bumps and so on. While this is ‘perceptual’, our goal was to achieve the inverse of this operation i.e teach a humanoid robot to synthesize these primitive shape critical points, and hence enable to learn the grammar to generate a wide gamut of trajectories in different contexts. From the action generation perspective, in a recent work we have shown how it is possible to teach iCub to generate all the shape CP’s derived in [6, 7].
3) Imposing context, towards ‘Goal Dependent’ motor action: Since ‘shape’ is conserved during coordinate transformation, scaling or the end effector employed, acquiring the motor knowledge of synthesizing shapes gives iCub the capability to generate a wide range of movement trajectories based on the context. So when iCub draws a curve like ‘C’ with a paint brush or bimanually maneuvers the steering wheel of the crane toy, both result in trajectories that result in same shape representations (in this case, curves of type ‘E-B-E’). For any other skill that requires synthesis of trajectories with these shapes (like steering the crane toy), the VTGS can just collect the information from the shape library, scale it to context and generate the virtual trajectory. Same is the case with actions like screwing, unwinding, cycling etc that also result in same shape representations (curved trajectories) in different context, serving different utilities, for which the motor knowledge can be reused.
4) Virtual Trajectories: Decoupling ‘Action’ from the ‘Actor’: While the visual shape extraction system transforms a continuous trajectory of the teacher into a discrete set of shape critical points, the virtual trajectory generation system does the inverse operation. In other words, it transforms the discrete set of shape critical points described in the motor goal into a continuous set of equilibrium points (that act as moving point attractor to the PMP based internal body model and trigger the synthesis of motor commands to perform the action ). The interested reader may refer to [6] for a detailed explanation of how virtual trajectories for the 12 primitive shape critical points are learnt. A central idea here is that since more complex trajectories can be ‘decomposed’ into combinations of primitive shape CP’s using CT, inversely can the motor actions needed to create them be ‘composed’ using combinations of the corresponding ‘learnt’ primitive actions. Rather, that they act as an attractors to the internal (body+ tool) model involved in action generation and play a crucial role in deriving the motor commands needed to create the shape.
5) From virtual trajectory to Motor Commands: Linking redundancy to Task dynamics, Timing & synchronization: The virtual trajectory synthesized by the VTGS is coupled to the appropriate internal body (body + tool) model to now synthesize the motor commands taking into account task dynamics. The Passive Motion Paradigm based forward inverse model for iCub upper body is used in this phase for action generation [3-5]. The interaction between PMP and VTGS is similar to the coordination of the movement of a puppet by a puppeteer. As the virtual trajectory pulls the relevant end effector in a specific fashion, the rest of the body (arm and waist joints) elastically reconfigures to allow the end effector to track the evolving virtual trajectory. When motor commands synthesized by this process of passive relaxation are actively fed to the robot, it reproduces the movement, hence generating the motor action.When the teacher demonstrates iCub to bimanually steer the crane toy (figure 2, Panel F-J), by gradually moving from the visual observation of teachers trajectory to its shape, collecting knowledge to generate that shape from the shape library (in this case acquired while learning to draw), synthesizing a virtual trajectory fitted to context, coupling the virtual trajectory to both arms (using PMP), iCub is able to swiftly maneuver the crane toy like the teacher demonstrated. From its own actions with the tool, it then learns the ‘tool jacobian’ i.e change in the magnetized tool tip position of the crane toy as a result of the change in its end effector position. The tool jacobians when coupled with the jacobians of the upper body using PMP allows iCub to maneuver the crane toy in a goal directed fashion. In this way motor knowledge acquired while learning the drawing skills can be systematically reused by iCub to swiftly learn to steer the crane toy in a goal directed fashion.
2. CONCLUSION
A wide range of human actions result in formation of trajectories that ultimately result in similar ‘shape’ representations. Most important among them are line, bump and cusp critical points described in [1-2]. For example, drawing a circle, driving a steering wheel, uncorking, winding, cycling, stirring etc are actions that have ‘circularity’ as invariant in them. If we teach a humanoid robot to synthesize ‘Shapes’ [6], we can endow then with the powerful capability to ‘compose, recycle’ the previously acquired motor knowledge to swiftly learn wide range of other motor skills. Is ‘shape’ the invariant through which humans imitate/mime effortlessly and instantaneously? Future research in this direction will be aimed at answering/validating these questions.
Acknowledgements
The research presented in this article is being conducted was conducted under the framework of EU FP7 projects iTalk (Grant no: FP7-214668) and DARWIN (Grant No: FP7-270138). The authors thank the European commission for the sustained financial support and encouragement.
References
[1] R. Thom (1975). Structural Stability and Morphogenesis. Benjamin, Reading, MA: Addison-Wesley.
[2] V. S. Chakravarthy, B. Kompella (2003). The shape of handwritten characters, Pattern recognition letters, Volume 24, pp. 1901-1913.
[3] Mussa Ivaldi, F. A., Morasso, P. & Zaccaria, R. (1988). Kinematic Networks. A Distributed Model for Representing and Regularizing Motor Redundancy. Biological Cybernetics, 60, 1-16.
[4] V. Mohan, P. Morasso, G. Metta, G. Sandini (2009). A biomimetic, force-field based computational model for motion planning and bimanual coordination in humanoid robots. Autonomous Robots, Volume 27, Issue 3, pp. 291-301.
[5] P.Morasso, M.Casadio, V.Mohan, J.Zenzeri (2010). A neural mechanism of synergy formation for whole body reaching. Biological Cybernetics, 102(1), 45-55.
[6] V. Mohan, G. Metta, J. Zenzeri, P. Morasso, V.S.Chakravarthy, G.Sandini (2010) Teaching a humanoid robot to draw 'shapes'. Autonomous Robots (in press).
[7] V. Mohan, G. Metta, J. Zenzeri, P. Morasso (2010) Teaching humanoids to imitate 'shapes' of movements. In Proceedings of the 20th international conference on Artificial neural networks: Part II (ICANN'10), Konstantinos Diamantaras, Wlodek Duch, and Lazaros S. Iliadis (Eds.). Springer-Verlag, Berlin, Heidelberg, 234-244.
Keywords:
Catastrophe theory,
Compositional Actions,
iCub Humanoid,
Passive Motion Paradigm,
Skill transfer
Conference:
IEEE ICDL-EPIROB 2011, Frankfurt, Germany, 24 Aug - 27 Aug, 2011.
Presentation Type:
Poster Presentation
Topic:
Architectures
Citation:
Mohan
V,
Morasso
P and
Metta
G
(2011). What does learning to ‘draw a circle’ have to do with driving, cycling, unwinding and screwing?.
Front. Comput. Neurosci.
Conference Abstract:
IEEE ICDL-EPIROB 2011.
doi: 10.3389/conf.fncom.2011.52.00028
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Received:
11 Apr 2011;
Published Online:
12 Jul 2011.
*
Correspondence:
Dr. Vishwanathan Mohan, Italian Institute of Technology, Robotics, Brain and Cognitive Science, Genoa, Italy, vishwanathan.mohan@essex.ac.uk