Motor Skill as Dynamic Constraint Satisfaction

Most of the above phenomena can be explained by bad usage of muscles. In the trivial case, the bad usage of muscles comes from simultaneous activation of antagonizing muscles. It happens even during such a simple task as continuous bowing on the same string for very beginners. Also quite experienced amateur players commit the error when the task become complicated; jumping to a far apart high position while playing a legato phrase, moving left hand fingers independently in a fast passage, rapidly changing bowing direction, and so on. Let us explain the case of jumping a far apart high position while playing a legato phrase. It occured to one of the authors when he was playing Elgar's small piece called ``Salute d'Amour''. It requires to jump from D to B on A string. Since the phrase requires vibrato and legato, one has to keep generating sound as long as possible before the jump and it is best realized by fixing the left hand position. Then sudden position change is required. The rapid state transition causes the above difficulty since antagonizing muscles tend to work simultaneously during the transition phase. Very recently, he also found the right hand problem; the conflict of muscles usage between playing on a single string and change of string. The former requires to control the right arm to keep on the same horizontal plane associated with each string whereas the latter requires a rapid vertical movement from one plane to another.

Another kind of difficulty is the last one in the above list: playing a very fast passage. Let us consider the right hand movement when playing a fast passage requiring rapid repetitive changes in bowing direction. Since the arm movement can be modeled by a pendulum osscilation, a proper osscilation frequency associated with the arm pendulum determines its natural frequency. Sometimes the frequency is too low to achieve a rapid repeated up and down movement. This causes the problem. In this case, we need to change arm pendulum's proper osscilation frequency.

Both of the difficulties can be described as constraint satisfaction problems. In the former case, the constraint to be satisfied is to avoid simultaneous use of antagonizing muscles and use of muscles to prevent natural counter movement against the main movement due to action-reaction law. The latter constraint is to satisfy natural physics of osscilation of the physical system consisting of our body and arm.

The real solution is to loosen only those muscles which are antagonistic to the muscles being used for changing the string, and move the entire arm. Up/down bowing and string changing can be regarded as horizontal and vertical movements, respectively. Therefore, if one can use different set of muscles for horizontal movement from those for vertical movement, one can loosen only some of those muscles for vertical movement. This avoids the problem of too much loosening of force which causes the tone discontinuity.

Another example of easy (but incorrect) solution for a simple task is jumping to a far high position by intercepting vibrato and continuous sound generation. This problem can also be solved by differentiating those muscles necessary for jumping to high position to those for making vibrato and fingering.

Practice is a conscious activity paying attention to satisfy constraints. For a sequence of constraints needed to perform a music note, a careful planning is neccesary for preparing best posture for each component task. During the practice, you may find some places which are difficult to play. In most cases, the difficulties come from the fact that there are complex tasks with many constraints to be satisfied simultaneously or in sequence to follow the music. Then, careful considerations and plannings are required to achieve the target of the performance while satisfying associated constraints.

Skill acquisition is the result of repeated practices to perform while keeping to satisfy constraints unconsciously or subconsciously. Professional players have acquired such skill for dynamically satisfying constraints. The unconscious process of achieving dynamic constraints satisfaction suggests that it is stored in the brain as a set of basic motor skill programs. Note that unbelievable skill comes from only repeated training while satisfying associated constraints. Amateur players often imagine to be able to acquire such skill by simple repeated training but in most cases it results in nothing. This implies the importance of constraints satisfaction.

For the future research, we are planning to collect data from extensive experimentation and to extract professional skill by applying data mining algorithms. We regard the extraction of professional skill as discovering constraints from performance data. We also aim to verbalize tacit knowledge of skill by machine learning. For this purpose, Inducitve Logic Programming (ILP) seems very promising because constraints can be expressed as a set of (negative) logical formula.

Using ILP to learn constraints leads us to consider an extension of behavioural cloning. We envisage using this framework to detect differences in skill between performers, for example comparing a teacher with a student. The teacher acts as a provider of performance data from which a constraint theory is induced. Data for the same piece is then obtained from a student. Where the student's performance data violates the constraints we detect a departure from the model of skill exemplified by the teacher.