Grasping versus Knitting: a Geometric Perspective

📝 Abstract

Grasping an object is a matter of first moving a prehensile organ at some position in the world, and then managing the contact relationship between the prehensile organ and the object. Once the contact relationship has been established and made stable, the object is part of the body and it can move in the world. As any action, the action of grasping is ontologically anchored in the physical space while the correlative movement originates in the space of the body. Evolution has found amazing solutions that allow organisms to rapidly and efficiently manage the relationship between their body and the world. It is then natural that roboticists consider taking inspiration of these natural solutions, while contributing to better understand their origin.

💡 Analysis

Grasping an object is a matter of first moving a prehensile organ at some position in the world, and then managing the contact relationship between the prehensile organ and the object. Once the contact relationship has been established and made stable, the object is part of the body and it can move in the world. As any action, the action of grasping is ontologically anchored in the physical space while the correlative movement originates in the space of the body. Evolution has found amazing solutions that allow organisms to rapidly and efficiently manage the relationship between their body and the world. It is then natural that roboticists consider taking inspiration of these natural solutions, while contributing to better understand their origin.

📄 Content

Grasping versus Knitting: a Geometric Perspective
Comment on Hand synergies: Integration of robotics and neuroscience for understanding the control of biological and artificial hands, by M. Santello et al.

Grasping an object is a matter of first moving a prehensile organ at some position in the world, and then managing the contact relationship between the prehensile organ and the object. Once the contact relationship has been established and made stable, the object is part of the body and it can move in the world. As any action, the action of grasping is ontologically anchored in the physical space while the correlative movement originates in the space of the body. Robots—as any living system—access the physical space only indirectly through sensors and motors. Sensors and motors constitute the space of the body where homeostasis takes place. Physical space and both sensor space and motor space constitute a triangulation, which is the locus of the action embodiment, i.e. the locus of operations allowing the fundamental inversion between world-centered and body-centered frames. Referring to these three fundamental spaces, geometry appears as the best abstraction to capture the nature of action-driven movements. Indeed, a particular geometry is captured by a particular group of transformations of the points of a space such that every point or every direction in space can be transformed by an element of the group to every other point or direction within the group. Quoting mathematician Poincaré, the issue is not find the truest geometry but the most practical one to account for the complexity of the world1. Geometry is then the language fostering the dialog between neurophysiology and engineering about natural and artificial movement science and technology. Evolution has found amazing solutions that allow organisms to rapidly and efficiently manage the relationship between their body and the world2. It is then natural that roboticists consider taking inspiration of these natural solutions, while contributing to better understand their origin.

The recent European project The Hand Embodied is a remarkable application of this multidisciplinary research paradigm3.

The human hand is certainly the most sophisticated organ evolution has provided to allow a living system to act on the world. The hand is recognized as a fundamental component of intelligence. Its richness comes from its extraordinary capacity to perform a large range of dexterous manipulation tasks ranging from hammering to knitting.
Hammering required maintaining a stable grasp between the handle and the moving arm. How to configure all the degrees of freedom of the hand around the handle, and what configurations obey the better the physical constraints of hammering (e.g. non sliding and force resistant contacts)? They are challenging questions even for a simple hammering task. Knitting is a task much more complicated that hammering. Knitting requires mobile dexterity. Finger movements have to be coordinated in order to steer the thread along the needles while tuning its tension. With respect to hammering, knitting adds another level of challenge. Complexity arises both from the dimension of

1 H. Poincaré, L’espace et la géométrie, Revue de métaphysique et de morale, 1895, vol. III, p. 631-646. 2 A. Berthoz, Simplexity: Simplifying Principles for a Complex World, Yale Univ. Press, 2012. 3 M. Santello et al. Hand synergies: Integration of robotics and neuroscience for understanding the control of biological and artificial hands, Physics of Life Reviews, 2016.
Appeared in Physics of Life Reviews (April 2016) the hand control space and from the dimension of the task as defined in the physical space.

Grasping an object goes back to establish and maintain a fixed relation between an arbitrary object frame and an arbitrary hand frame. Grasping task and its physical constraints is then described in the physical space by the space of hand placements, i.e. a space of dimension 6. Considering the many possible postures of the hand (i.e. the many placement of the fingers around the object), the question of grasping is to select the ones that fitful the constraints. The link to be settled is between a six dimensional space and the hand high dimensional configuration space. Many hand postures might be admissible and many movements reaching an admissible posture might be feasible. The hand is said to be redundant with respect to grasping task. Redundancy requires methods for posture and movement selection. Posture and movement spaces are highly dimensional spaces. Their dimensions give a measure of the computational complexity of the task. All current researches in life science as well as in engineering explore how living and artificial systems face such a complexity. Both understanding the computation foundations of actions performed by a

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