In order to effectively reach and grasp an object, we need to solve the inverse kinematics problem, i.e., the coordinate transformation from the visual coordinates to the joint angle vector coordinates of the arm. An important topic in neuroscience is the study of the learning mechanisms involved in solving the human inverse kinematics. We conducted interviews with five pediatricians about the motor function of infants suffering from serious upper limb disabilities. The doctors stated that the infants were still able to touch and stroke an object without hindrance. In one case, an infant without a thumb had a major kinematically influential surgical operation, transplanting an index finger as a thumb. After the operation, the child was able to learn how to use the index finger like a thumb. In order to better understand the human motor learning capability, we believe that the coordinate transformation learning of the human inverse kinematics solver is necessary.
Although a number of learning models of the inverse kinematics solver have been proposed, a definitive learning model has not yet been obtained. This is from the point of view of the learning capability of the learning model, the structural complexity of the learning model, and the biological plausibility of the employed hypothesis.
The conventional learning models of the inverse kinematics have a number of shortcomings. The Direct Inverse Modeling approach employed by many researchers is not applicable to the inverse kinematics model learning of a human arm that has redundancy. Since the Forward and Inverse Modeling approach proposed by Jordan and the Feedback Error Learning approach proposed by Kawato are both based on the local information of the controlled system, these methods do not always result in a precise inverse kinematics model, given poor initial status. Furthermore, such conventional methodologies do not fully consider the discontinuity of the inverse kinematics system of the human arm with joint limits. It is difficult for a traditional multi-layer neural network to approximate the discontinuous inverse kinematics function of the human arm. An accurate inverse kinematics model for the overall hand position and orientation cannot be obtained using the conventional learning methods.
The conventional learning models have a number of drawbacks as biological models, as well as the functional drawbacks. Direct Inverse Modeling requires the complex switching of the input signal of the inverse model. When the hand position control is performed, the input of the inverse model is the desired hand position, velocity, or acceleration. When the inverse model learning is performed, the input is the observed hand position, velocity, or acceleration. Although the desired signal and the observed signal could coincide, the characteristics of the two signals are very different. So far, no researcher has been able to successfully model the switching system. Forward and Inverse Modeling approach requires the back-propagation signal, a technique that does not have a biological basis. That model also requires the complex switching of the desired output signal for the forward model. When the forward model learning is performed, the desired output is the observed hand position. When the inverse kinematics solver learning is performed, the desired output is the desired hand position. We believe that the complex signal switching required by Direct Inverse Modeling or Forward and Inverse Modeling does not occur in the relatively low level sensory-motor learning of the human nervous system. In addition, the Feedback Error Learning requires a pre-existing accurate feedback controller.
It is necessary for any proposed learning model to possess a number of characteristics: (1) it can explain the human learning function, (2) it has a simple structure, and (3) it is biologically plausible. In this research, novel learning models for the human inverse kinematics solver are proposed and the feasibility of the proposed models are illustrated by using numerical simulations.
The first goal of this research is to propose a novel learning model of coordinate transformation of the human hand position feedback controller. This research presents two biologically plausible learning models of coordinate transformation function of the feedback controller. The first model is based on the disturbance noise in the hand position control loop and the feedback error signal. The second model is based on the change of the hand position error. The proposed learning models are capable of learning an accurate inverse kinematics solver without using a forward model, a back-propagation signal, or a pre-existing feedback controller. The feasibility of the proposed learning models is illustrated using numerical simulations.
Since a human can approximately solve inverse kinematics problems without using the visual feedback of hand position, it is clear that the human nervous system employs inverse kinematics model. However, it is difficult for a standard multi-layer neural network to approximate a multi-valued and discontinuous inverse kinematics function of a human arm. The second goal of this research is to propose a novel learning model of the inverse kinematics model of the human arm. Although the inverse kinematics function of the human arm is a multi-valued and discontinuous function, the inverse kinematics function can be constructed by the appropriate mixture of continuous functions. A novel modular neural network architecture that can learn a discontinuous inverse kinematics function by the appropriate switching of multiple neural networks is proposed. The performance of the proposed neural net system is illustrated through numerical experiments.