CC BY
7Adaptive control for athletic motor skills excellence
UDC 796.012
Dr.Hab., Professor V.I. Zagrevskiy1, 3
Dr. Hab., Professor O. I. Zagrevskiy2, 3
1Mogilev State A. Kuleshov University, Mogilev, Belarus
2Tyumen State University, Tyumen
3National Research Tomsk State University, Toms^
Corresponding author: zvi@tut.by
Abstract
Objective of the study was to develop adaptive control software to model movement of an object from the initial phase when the execution deviates from the execution standard to the required standard state with the relevant kinematics.
Methods and structure of the study. The research methods applied during the study were as follows: system-structural analysis of movements, theory of automatic control, simulation of motions with a computer. The object of study was the adaptive control over the biomechanical system, driving the object of movement from the given startup state to the required final state. Materials: computer model of the movement, organization of research - computational experiments conducted on the basis of the original software program (algorithmic programming language VisualBasic 2010 Express, integrated programming environment - VisualStudio 2013).
Results and conclusions. The computational experiments showed that the adaptive control model built on the feedback law in the controlled phase coordinates and time successfully solves the problem of putting the object of movement with "erroneous" trajectory back on the given programmed trajectory with the achievement of the required kinematic parameters by the final time.
Keywords: athletic performance, execution standard, execution error, motor skill, adaptive control, biomechanical system trajectory.
Background. It is the deviation of the kinematic parameters of the current biomechanical system trajectory from the execution standard ('programmed strategy') that results in serious technical errors and, when the deviation is significant, failed athletic performance. As far as the athletic performance quality is concerned, it is the athlete who takes efforts to correct a deviation of the actual execution from the execution standard that is referred to as the execution error [2, 3]. The study considers a computerized adaptive control model to prevent potential execution error and help the subject come back to the execution standard. In contrast to the relevant prior study [4], the programmed trajectory kinematics herein include not only the subject's coordinates but also their first and second derivatives - to help synthesize a wide range
of movement sequences: from striking contact to super soft touch.
Objective of the study was to develop adaptive control software to model movement of an object from the initial phase when the execution deviates from the execution standard to the required standard state with the relevant kinematics.
Methods and structure of the study. We used methods of systemic movement structure analysis, automatic control theory based methods, and movement modeling/ simulation computer methods. We used the following variables to describe the object kinematics from the initial (T0) to final (Tk) time moments: S0 is the initial coordinate, V0 is the initial velocity, Sk is the final coordinate, and Vk is the final velocity.
Let us consider the case of the approach closed in time [1], with movement in the time interval [T0 to Tk] geared to move the control object from the initial point with the phase coordinates S0, V0 to the final points with coordinates Sk,Vk. Let's synthesize control in acceleration units. When S is the object movement, £ the second derivative of S by time (t), then
&& (1) S = u.
Programmatic control (u) under two final conditions may be described by the following function with two unknown parameters (C0, C1):
u = C0 + Cjt.
(2)
u is the control function; and ttime.
-o rp 2 T2 T 3
Vk = V + C0Tt + ^, = S0 + V0Tk + CoT- +
(3)
6 s
AT2 AT2 AT AT
6 Sc AV 2VC
The current phase coordinates of the key point (Sc, Vc) before the controlled object with the time interval AT may be computed as recommended in [1] as follows:
Vc= V0 + C0(t + AT)+C+^ATf ,
Sc= S0 + V0(t + AT ) +
C0(t + AT )2 C(t + AT )3
6 Sk _ AT2 AT + C0 kl = 6V0 AT2 4 C0 + —+ C, AT k = 2 AT2 2C t-—L. AT ■
C AT2 ■ k„ i S 6 ~~~ÄT2 ■ kV 4 = AT ' (8)
To find the final velocity (Vk) and coordinate (Sk,) let's put (2) into (1) and by integrating it twice within the limits [T0, Tk], arrive at
Adaptive control will drive the object from the deviated trajectory (resulting from execution error) to the standard execution trajectory. Let us design the adaptive control system with a feedback capacity [1]: when the current situation (SC, VC) with the time tag t is initial, then
Note that AT (control rigidity) varies within the range of 10-25% of Tk. The shorter is AT, the faster the object comes back from the deviated trajectory to the standard one.
Computational experiments were run using the original basic computer software (in VisualBasic 2010 Express using VisualStudio 2013 toolkit) and were intended to rate efficiency of the software system in synthesizing the adaptively controlled object movement.
Results and discussion. We run a computational experiment to rate benefits of the software system.
1. Movement with a preset execution standard.
Initial data: timeframe T0 = 0, Tk = 20, AT = 3. Spatial-temporal variables: S0=200, V0=10, Sk=0. Given on Figure 1 hereunder is the visualized computation result.
2. Movement with synthesized adaptive control.
For the initial time moment, the execution error i.e. the difference between the actual execution and execution standard may be discretional, e.g. AS0 = 200-170=30, AV0 = 10-6=4. Initial data: timeframe T0 = 0, (4) Tk = 20, AT = 3. Spatial-temporal variables: S0 = 170, V0 = 6, Sk = 0. As a result, the ratios (k) in the adaptive control algorithm (7) and control function (u) are as follows
k0 =51,000; k =-1,150; k2 =-0,420; + = 0,180; k = -0,800; kS = -0,240
(5) u = 51 -1,15?-0,41?2 +0,018^-0,24^ - 0.8K
The current time t varies within the frame [0, T], while C0, C1, knowing the initial and final coordinates and object velocity, are computed as follows
ÔS^ +
T 2 + T 2
4V0 2Vk
c = 12Sl _ 12S*. + + 6Vl
i t 3 T 3 T 2 T 2
(6)
Let's substitute (6) into (5) with mathematical operations to arrive at the following adaptive control law:
u = k0 + kxt + k2t2 + k3t3 + kSS + kVV. (7)
Note that ratios (k) in equation (6) are computed once for the whole movement trajectory as follows:
The computational experiments showed that the adaptive control with a feedback capacity designed using the phase coordinates and timeframe is highly efficient in forcing the controlled object back from the deviated/ erroneous trajectory to the execution standard with the target kinematics at the final time point (Figure 2).
Conclusion. The adaptive control law (7), was found efficient in forcing the controlled object to follow the execution trajectory within the preset timeframe [T0,Tk] to drive it at the final phase point (Sk, Vk).
The feedback capacity with phase coordinates within the adaptive control law ensures the controlled object coming back from the erroneous trajectory (resulting from execution error) to the execution standard.
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Theory and Practice of Physical Culture I teoriya.ru I October № 10 2020
A - standard ( —— (* * * * ) execution
■ ) and adaptively controlled
B - velocity of the standard ( ——and adaptively controlled (♦ ■ ♦ • ) execution
C - acceleration of the standard ( ——-) and adaptively controlled (■ ■ ■ • ) execution
D - phase coordinates in the standard ( ——-) and adaptively controlled (■ ■ ■ • ) execution
Figure 1. Trajectory (coordinates, velocities, accelerations) of the standard and adaptive control execution Standard and adaptive control execution (A, B, C) kinematics and synthesized movement trajectory (D)
The adaptive control law (7) with both the feedback capacity and phase coordinates corrects every deviation of the controlled object from the execution standard, with the correction speed determined by AT.
Variations in the movement conditions make no changes to the adaptive control law but form a new adaptive control adjusted to the new conditions to attain the movement target by the final time point. The adaptive control with feedback capacity acts as an execution error correction tools that drives the controlled object back to the standard execution trajectory.
References
1. Batenko A.P. Control of final state of moving objects. Moscow: Sov. Radio publ., 1977. 250 p.
2. Gaverdovskiy Yu.K. Sports training. Biomechanics. Methodology. Didactics. Moscow: Fizkultura i sport publ., 2007. 912 p.
3. Golovko D.E., Zagrevskaya A.I. Individual kinesiologi-cal resource mobilizing in training process. Teoriya i praktika fiz. kultury. 2019. No. 11. pp. 80-82.4.
4. Zagrevskiy V.I., Zagrevskiy O.I. Motor errors compensating adaptive control model in exercise kinematics. Teoriya i praktika fiz. kultury. 2019. No. 10. pp. 44-46.
