Neural Dynamics Variations Observer Designed for Robot Manipulator Control Using a Novel Saturated Control Technique

Abstract

This work presents a novel controller for the dynamics of robots using a dynamic variations observer. The proposed controller uses a saturated control law based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="normal">sin</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msup><mml:mrow><mml:mtext>tg</mml:mtext></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced></mml:math> function instead of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="normal">tanh</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mfenced></mml:math>. Besides, this function is an alternative to the use of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi mathvariant="normal">tanh</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mfenced></mml:math> in saturation control, since it reaches its maximum value more gradually than the hyperbolic tangent function. Using this characteristic, the transition between states is smoother, with similar accuracy to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi mathvariant="normal">tanh</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mfenced></mml:math>. The controller is designed using a saturated SMC (sliding mode controller) and a dynamic variations observer based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mi mathvariant="normal">GRNN</mml:mi></mml:math> (general regression neural network). The originality of this work is the use of a combination of adaptive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mi mathvariant="normal">GRNN</mml:mi></mml:math> with a sliding mode controller (SMC) including a new saturation function. Finally, experiments based on trajectory tracking demonstrate the robustness and simplicity of this method.