# Sensorimotor Control Using Adaptive Neuro-Fuzzy Inference for Human-Like Arm Movement
###### Abstract
They employ a feedback approach from task space to joint space to accomplish a motion task, incorporating linear joint angular velocity feedback without solving inverse kinematics. [PERSON] et al. [21] design a task-space feedback controller including the nonlinear muscle model characteristics for the reaching movements. The desired trajectory is formulated within the task space, and the controller is designed using muscle-space parameters, such as muscle length and contractile velocity. These muscle-space variables are obtained by performing inverse kinematics, transitioning from the task space to the muscle space. Since the motion of the musculoskeletal system can be represented in various spaces, including muscle space, joint space, and task space, the effectiveness of the controller is impacted by the choice of the space in which the controller is designed. In order to improve the control design performance of the approach suggested in [21], as well as its robustness against possible noise sources, an iterative learning control algorithm using plural space variables is introduced in [22]. Two studies [23; 24] introduce adaptive robust control designs for the humanoid robot arms with biarticular muscles to handle the effects of the uncertain dynamic parameters and disturbances. The adaptive algorithms introduced in [23; 24] update the dynamics parameters online and handle the dynamic parameter perturbation and disturbance during the movement. An adaptive optimal multi-critic based controller is designed in [25] for a multi-input multi-output musculoskeletal arm model. The fundamental concept behind the design of the adaptive optimal control is to possess the ability to adapt to dynamic parameter changes while determining the muscle force optimized in real-time. Because of the real-time responsiveness and robustness against the uncertainties in sliding mode control architectures, [PERSON] et al. [26] employ a trajectory tracking control utilizing a switched sliding mode controller in a manipulator powered by pneumatic artificial muscles and [PERSON] et al. [27] introduces an adaptive fuzzy sliding mode control approach to track the elbow joint and endpoint of the human arm. It is important to remark that most existing model-based controllers have used a simplified version of the musculoskeletal system and such model simplification might not replicate the full range of human movements with high fidelity. For details on musculoskeletal control, the reader is referred to [28]. The main objective of this paper is to outline an effective control strategy that mimics human movement. This paper proves that the developed controller identifies the necessary muscle activation that minimizes the force discrepancy between muscle and arm movement models about the null-space vector. A Hill-type muscle model is employed in a three-link musculoskeletal model with nine muscles in a curved arrangement, including six monoarticular muscles that cross multiple/two joints and three biaarticular muscles responsible for shoulder, elbow, and wrist joint movement. The calculation of muscle activation has two components: the model-based joint space controller term and the null-space term, determined via a model-free learning algorithm. The null-space term plays a significant role in rendering the movement more human-like, and it is typically considered as a constant rather than being calculated from real-time motion data. The approach in this study to ascertain the suitable null-space term involves reducing the force difference between the muscle and arm movement models using the Adaptive Neuro-Fuzzy Inference System (ANFIS). An assemblage of exemplars with a three-link arm has been incorporated to illustrate the application of the developed control algorithm. The simulation results have also been included to corroborate the performance quality of the proposed control methodology. The rest of this work is organized as follows. Section 2 introduces a kinematic and dynamic model of the musculoskeletal arm model.