Eri Nakano

Internal forward models in the cerebellum: fMRI study on grip force and load force coupling.

Internal models are neural mechanisms that can mimic the input-output or output-input properties of the motor apparatus and external objects. Forward internal models predict sensory consequences from efference copies of motor commands. There is growing acceptance of the idea that forward models are important in sensorimotor integration as well as in higher cognitive function, but their anatomical loci and neural mechanisms are still largely unknown. Some of the most convincing evidence that the central nervous system (CNS) makes use of forward models in sensory motor control comes from studies on grip force-load force coupling. We first present a brief review of recent computational and behavioral studies that provide decisive evidence for the utilization of forward models in grip force-load force coupling tasks. Then, we used functional magnetic resonance imaging (fMRI) to measure the brain activity related to this coupling and demonstrate that the cerebellum is the most likely site for forward models to be stored.

A Kendama learning robot based on bi-directional theory

A general theory of movement-pattern perception based on bi-directional theory for sensory-motor integration can be used for motion capture and learning by watching in robotics. We demonstrate our methods using the game of Kendama, executed by the SARCOS Dextrous Slave Arm, which has a very similar kinematic structure to the human arm. Three ingredients have to be integrated for the successful execution of this task. The ingredients are (1) to extract via-points from a human movement trajectory using a forward-inverse relaxation model, (2) to treat via-points as a control variable while reconstructing the desired trajectory from all the via-points, and (3) to modify the via-points for successful execution. In order to test the validity of the via-point representation, we utilized a numerical model of the SARCOS arm, and examined the behavior of the system under several conditions. Copyright 1996 Elsevier Science Ltd.

Quantitative examinations for multi joint arm trajectory planning — using a robust calculation algorithm of the minimum commanded torque change trajectory

In previous research, criteria based on optimal theories were examined to explain trajectory features in time and space in multi joint arm movement. Four criteria have been proposed. They were the minimum hand jerk criterion (by which a trajectory is planned in an extrinsic-kinematic space), the minimum angle jerk criterion (which is planned in an intrinsic-kinematic space), the minimum torque change criterion (where control objects are joint links; it is planned in an intrinsic-dynamic-mechanical space), and the minimum commanded torque change criterion (which is planned in an intrinsic space considering the arm and muscle dynamics). Which of these is proper as a criterion for trajectory planning in the central nervous system has been investigated by comparing predicted trajectories based on these criteria with previously measured trajectories. Optimal trajectories based on the two former criteria can be calculated analytically. In contrast, optimal trajectories based on the minimum commanded torque change criterion are difficult to be calculated, even with numerical methods. In some cases, they can be computed by a Newton-like method or a steepest descent method combined with a penalty method. However, for a realistic physical parameter range, the former becomes unstable quite often and the latter is unreliable about the optimality of the obtained solution. In this paper, we propose a new method to stably calculate optimal trajectories based on the minimum commanded torque change criterion. The method can obtain trajectories satisfying Euler-Poisson equations with a sufficiently high accuracy. In the method, a joint angle trajectory, which satisfies the boundary conditions strictly, is expressed by using orthogonal polynomials. The coefficients of the orthogonal polynomials are estimated by using a linear iterative calculation so as to satisfy the Euler-Poisson equations with a sufficiently high accuracy. In numerical experiments, we show that the optimal solution can be computed in a wide work space and can also be obtained in a short time compared with the previous methods. Finally, we perform supplementary examinations of the experiments by Nakano, Imamizu, Osu, Uno, Gomi, Yoshioka et al. (1999). Estimation of dynamic joint torques and trajectory formation from surface electromyography signals using a neural network model. Biological Cybernetics, 73, 291-300. Their experiments showed that the measured trajectory is the closest to the minimum commanded torque change trajectory by statistical examination of many point-to-point trajectories over a wide range in a horizontal and sagittal work space. We recalculated the minimum commanded torque change trajectory using the proposed method, and performed the same examinations as previous investigations. As a result, it could be reconfirmed that the measured trajectory is closest to the minimum commanded torque change trajectory previously reported.

Composition and decomposition learning of reaching movements under altered environments: An examination of the multiplicity of internal models

We have studied the learning processes of reaching movements under novel environments whose kinematic and dynamic properties are altered. In the experiments, we have used, as the kinematic transformation, a rotational transformation which is displayed by rotating a cursor indicating hand position in the orthogonal coordinate system on a CRT; a viscous transformation using viscous field as the dynamic transformation; and a combined transformation of these two transformations. It is observed that the hand trajectory approaches a straight line along with learning and accurately reaches the target. When the combined transformation is learned after the rotational transformation and viscous transformation are learned first, respectively, the final error becomes smaller and the path length also becomes shorter than the case when the combined transformation is learned first. Moreover, the final error and path length of the movement under rotational transformation and viscous transformation when the combined transformation is learned first also become smaller than the case when the rotational and viscous transformations are learned first. These results suggest that the central nervous system has learned separately the multiple internal models which compensate the respective transformations, and has composed or decomposed the respective internal models in accordance with the environmental changes. It may be considered that such multiplicity of internal models makes it possible for the living body to flexibly cope with the environments or tools having various dynamic and kinematic properties.

A Kendama learning robot based on a dynamic optimization theory

A general theory of movement pattern perception based on a dynamic optimization theory can be used for motion capture and learning by watching in robotics. We exemplify our methods for the game of Kendama, executed by the SARCOS Dextrous Slave Arm, which has exactly the same kinematic structure as a human arm. Three ingredients have to be integrated for the successful execution of this task. The ingredients were (1) to extract via-points from a human movement trajectory using a forward-inverse relaxation model, (2) to treat via-points as a control variable while reconstructing the desired trajectory from all the via-points, and (3) to modify the via-points for successful execution.

Multi Joint Arm Trajectory Formation Based on the Minimization Principle Using the Euler-Poisson Equation

In previous research, criteria based on optimal theories were examined to explain trajectory features in time and space in multi joint arm movements. Four criteria have been proposed. They were the minimum hand jerk criterion, the minimum angle jerk criterion, the minimum torque change criterion, and the minimum commanded torque change criterion. Optimal trajectories based on the two former criteria can be calculated analytically. In contrast, optimal trajectories based on the minimum commanded torque change criterion are difficult to be calculated even with numerical methods. In some cases, they can be computed by a Newton-like method or a steepest descent method combined with a penalty method. However, for a realistic physical parameter range, a former becomes unstable quite often, and the latter is unreliable about the optimality of the obtained solution. In this paper, we propose a new method to stably calculate optimal trajectories based on the minimum commanded torque change criterion. The method can obtain trajectories satisfying Euler-Poisson equations with a sufficiently high accuracy. In the method, a joint angle trajectory, which satisfies the boundary conditions strictly, is expressed by using orthogonal polynomials. The coefficients of the orthogonal polynomials are estimated by using a linear iterative calculation so as to satisfy the Euler-Poisson equations with a sufficiently high accuracy. In numerical experiments, we show that the optimal solution can be computed in a wide work space and can also be obtained in a short time compared with the previous methods.