A Computational Learning Approach for the Development of Karate Sequences

Karate, like most martial arts, relies on the development of complex sequences of interrelated techniques. The development of strong technique, physical endurance, mobility, and precision requires repetitive practice of sequences and combinations of moves. However, training typically has biases, leading to limited repertoire, and poor dynamical decision making. Here we use machine learning to develop a mathematical model of sequences of karate techniques. We present a series of algorithms for the generation of novel training combinations, which are internally consistent with a supplied training regime. Due to the general nature of the mathematical approach developed here, we anticipate our approach has wider applications, for example analysing indi-vidual competitors’ decision-making process and performance, identifying weaknesses and vulnerabilities in an athlete’s repertoire.


Introduction
The World Karate Federation (WKF) estimates that there are over 10 million athletes and 100 million karate practitioners worldwide (Stefano Vando et al., 2013), making karate one of the most popular martial art/combat sports (Koropanovski et al., 2011). At a competition level, Karate is divided into two different specialities: Kumite and Kata. Kumite (sparing) is non-contact combat between two opponents using punching, kicking, and striking techniques. Kata (forms) represents real combat with imaginary opponents. Both disciplines require an athlete to perform complex high momentum and velocity techniques with precision, requiring physical conditioning (particularly anaerobic capacity) DOI: 10.4236/ape.2021.114041 504 Advances in Physical Education (Beneke et al., 2004), postural control (Filingeri et al., 2012), tactical and technical skill (Cesari & Bertucco, 2008). Hironori Ōtsuka (2006), the founder of Wado-Ryu karate, emphasised that the athlete must be prepared to move or execute a strike in any direction at any moment in time. This requirement is reflected in both kumite and kata training.
Kumite engages an opponent, within a controlled combat environment. The dynamic nature of kumite ensures the athlete must be agile (changing direction in response to stimuli) and possess a high anaerobic capacity (Beneke et al., 2004). As the athlete engages their opponent, they will be required to both defend themselves against attacks and evade their opponent's defences in an effort to reach their target, in order to score points. Analysis of 1198 kumite sequences during the 1992 European championships found that 11.4% of combinations lasted between 1 -7 seconds, while 79.5% lasted between 8 -50 seconds (Sterkowicz & Franchini, 2009 By learning the statistical relationships between moves, and preserving those relationships in the generated sequences, the created combinations are internally consistent, yet novel, with the syllabus presented to the algorithm. The agnostic nature of the algorithm means there is no human bias towards preferred techniques or avoidance of difficult techniques. It is well recognized that when presented with a decision around actions, the psychology of humans will favour those (in this case) techniques that are familiar and present less risk.
The result is a more rounded training syllabus.
Aiding the coaches to understand the importance of certain sequences for learning purposes and to formulate an objective, stepwise approach to building motor skills in athletes.
Coaching the coaches, giving them a bigger set of sequences to choose between.
Provides a consistent tool for the development of sequences and progressions.
As an example, we will apply our approach to the development of training sequences that will support Wado-Ryu grading syllabus. The remainder of this paper is organized as follows. In the following section, we outline Renraku Waza, the data and mathematical approach to representing the relationship between moves, and finally, we present 3 algorithms for generating combinations of moves with various properties. In section 3, we provide some examples of the Renraku Waza generated by our approach. In section 4, we provide a discussion of the implications, applications and next steps in this research. Finally, in section 5, we provide some closing remarks.

Methods
During a kata or kumite bout, there are three possible situations an athlete could face: attack (kick, punch, advance…), defend (block, counter, tai sabaki…), and withdraw (turn, evade, retreat). Each of these situations, be it kata or kumite, change during a bout. The selection of techniques, timing, and postural control requires practice and experimentation and is taught within the context of a training syllabus for a particular style of karate. In this section, we develop a formal mathematical model of a syllabus. We then take the Wado-Ryu grading syllabus and encode it within the framework outlined here.

A Mathematical Model of Technique Sequences
We define a model of a collection of techniques, or syllabus, as a simplified finite state machine (Hopcroft & Ullman, 1979), that has a set of moves and a set of transitions between each move. Formally, the syllabus,  is a four-element tuple: As Green (1990) demonstrates, the set of production functions δ can be rewritten as a directed graph G. In formal terms, a digraph is an ordered pair ( )  Figure 1 illustrates how a sequence of moves is encoded into a graph, so the final model of a syllabus can be written as:

Data
Many styles of karate exist, but only four are recognised by the World Karate Another characteristic is its applied nature of the style, with the style taught as a progression from kihon to kata to kumite. Due to the applied nature of Wado-Ryu, each grade is required to display a set of competencies in Renraku Waza.
These competencies are clearly codified in the Wado-Ryu grading syllabus (MacClean, 1990 (Mudric & Rankovic, 2016). When punching to the head or body, for example, the location of the centre of mass changes relative to the limb length and height of the target, which changes the direction of centre of mass.

Encoding Data
Techniques that started a sequence were added to the set S I . While techniques that ended a sequence were added to the set S F . The graph G, was represented as an adjacency matrix M. Each combination of techniques within the syllabus was parsed, and the frequency of occurrence of each pair of techniques ( ) , i j s s was recorded in A ij . Once all pairs of techniques were parsed, the frequencies of occurrence were normalised into a probability of s j following s i : The resulting weighted graphy is shown below in Figure 2.

Generated Sequences
The model described in Equation (2)  , where the probability of taking arc i a , is defined by the weighted graph G. A simple approach to implementing a walk on G, is to adapt a depth first search (Knuth, 1997). As Knuth (1997) shows there are recursive and iterative algorithms for performing DFS; Algorithm 1 depicts a simple algorithm for performing a walk G. The major adaptation is the function ( ) i Γ s , that randomly selects the next node in the walk based on the weight of the arc i a .
As an illustration, Figure 3 shows the output of 10 runs of the algorithm, on the data provided.   From a cognitive developmental perspective, analysis of models of different skill levels, e.g. beginner to international competitor, would provide useful insight. The application of algorithmic information theory (Kolmogorov, 1963;Chaitin, 1966), would provide insights into the cognitive development of athletes, as well as the complexity of decision making of different skill levels and different athletes.  However, the body must have the conditioning to perform the sequences of movements that kata demands. By codifying and sequencing movement combinations according to the need of kata, these sequences can be taught to the athlete, who can then work on their specific areas of need. This has the advantages of improving their physical capability generally (improving their body's ability to perform the movements in sequence, which has transference to kumite) and of improving their kata specifically. Rather than focusing on the entire kata sequence, they can work on their body's movement efficiency outside of kata (but with movements that correspond to kumite), in a systematic, logical and applied manner.