According to the neuromuscular model of virtual trajectory control, the postures and movements of limbs are performed by shifting the equilibrium positions determined by agonist and antagonist muscle activities. In this study, we develop virtual trajectory control for the reaching movements of a multi-joint arm, introducing a proportional-derivative feedback control scheme. In virtual trajectory control, it is crucial to design a suitable virtual trajectory such that the desired trajectory can be realized. To this end, we propose an algorithm for updating virtual trajectories in repetitive control, which can be regarded as a Newton-like method in a function space. In our repetitive control, the virtual trajectory is corrected without explicit calculation of the arm dynamics, and the actual trajectory converges to the desired trajectory. Using computer simulations, we assessed the proposed repetitive control for the trajectory tracking of a two-link arm. Our results confirmed that when the feedback gains were reasonably high and the sampling time was sufficiently small, the virtual trajectory was adequately updated, and the desired trajectory was almost achieved within approximately 10 iterative trials. We also propose a method for modifying the virtual trajectory to ensure that the formation of the actual trajectory is identical even when the feedback gains are changed. This modification method makes it possible to execute flexible control, in which the feedback gains are effectively altered according to motion tasks.

This paper proposes an analysis of walking balance in terms of movements of stance and swing legs based on an inverted pendulum and a simple pendulum. Linearization, decoupling, and non-dimensionalization of a compass gait model enable to characterize the relationship of the trajectories between the stance and swing legs by only two parameters (energy ratio and phase difference). The energy ratio is defined by the ratio of the orbital energy between the pendulums. The phase difference represents the position of the stance leg in relation to the swing leg. This study considers an orbital energy conservation of a step transition and analyzes reachability of a desirable touchdown condition. If the time evolution from a current state is not reachable to the desired touchdown region, the state is labeled as a state in balance loss. By analyzing the reachability limits of the energy ratio and phase difference, we illustrate the balance loss and safe regions on the state space of the inverted pendulum, which is termed as balance map. We examined the effects of the simplification and linearization of the compass gait model by using computer simulations. Through the simulations of walking with perturbations, we confirmed that the balance map analysis could predict a future fall in an early phase for even trajectories derived by the nonlinear model.

It is well known that planar reaching movements of the human shoulder and elbow joints have invariant features: roughly straight hand paths and bell-shaped velocity profiles. The optimal control models with the criteria of smoothness or precision, which determine a unique movement pattern, predict such features of hand trajectories. In this letter on expanding the research on simple arm reaching movements, we examine whether the smoothness criteria can be applied to whole-body reaching movements with many degrees of freedom. Determining a suitable joint trajectory in the whole-body reaching movement corresponds to the optimization problem with constraints, since body balance must be maintained during a motion task. First, we measured human joint trajectories and ground reaction forces during whole-body reaching movements, and confirmed that subjects formed similar movements with common characteristics in the trajectories of the hand position and body center of mass. Second, we calculated the optimal trajectories according to the criteria of torque and muscle-tension smoothness. While the minimum torque change trajectories were not consistent with the experimental data, the minimum muscle-tension change model was able to predict the stereotyped features of the measured trajectories. To explore the dominant effects of the extension from the torque change to the muscle-tension change, we introduced a weighted torque change cost function. Considering the maximum voluntary contraction (MVC) force of the muscle as the weighting factor of each joint torque, we formulated the weighted torque change cost as a simplified version of the minimum muscle-tension change cost. The trajectories owing to the minimum weighted torque change criterion also showed qualitative agreement with the common features of the measured data. Proper estimation of the MVC forces in the body joints is essential to reproduce human whole-body movements according to the minimum muscle-tension change criterion.

In this paper, we propose a cooperative control of a wearable robot for paraplegics. The control system adjusts the stride length and walking velocity of a robot according to user's voluntary movement while generating a continuous walking pattern. We assume that the desired stride length and walking speed correspond to the preceding motion of a walking aid (walker), and the motion of the walker by the user was measured by a laser range sensor and an accelerometer. The continuous walking pattern during a step was planned by optimization of joint trajectories under inequality conditions. To perform continuous walking, the desired trajectory is required before the walker movement. To adjust the foot placement according to the walker movement, the desired walking pattern in the late swing phase is replanned. For the latest movement distance of the walker, the posture at heel strike is modified by Newton-like iterative calculations. We confirmed that a normal subject could walk continuously with a wearable robot controlled by our system while changing the stride length and walking speed.

In this paper, we propose an alternative motion planning method for a wearable robot with a variable stride length and walking speed. Trajectories are planned in a joint space rather than a workspace to avoid an ill-posed problem with no solution in inverse kinematics, and to consider the joint's range of motion, maximum velocity, foot clearance, and backward balance. The joint trajectories are represented by minimum jerk trajectories. Two via-points are assigned, and the parameters (angle and angular velocity) at the via-points are determined by applying an inverted pendulum model or optimization to satisfy the constraints. The fastest gait pattern generated by the proposed algorithm was twice as fast as the pattern generated by the workspace-based planning method. We confirmed that the fastest walking pattern of 0.36 m/s was feasible on a treadmill, and a walking pattern of 0.27 m/s was found for walking across the floor with a walker. Furthermore, the proposed method required approximately 65% of the electric power for the workspace-based method for the same walking speed and stride length. These results suggest that the proposed motion planning method is effective at generating a high-speed and efficient gait pattern for a wearable robot.

A legged locomotor device for paraplegics have been attempted to improve their ADL and to prevent some complications. A stride control of the system based on the user's intension is important to coordinate the voluntary movements of the user and the assisted movements of the paralyzed legs. In this paper, we propose a human interface with a walker to control the stride length of a legged locomotor device. Assuming that a intended stride is equal to a distance of the preceding movement of the walker, we developed a human interface estimating the movement distance of the walker, where the distance is calculated by polynomial fitting for the acceleration of the movement. In this study, we examine the proposed human interface from the measurement experiments of gait movements, and report the following results: (1) estimation accuracy by polynomial fitting method, and (2) feasibility of the adjustment of stride length using the proposed method. These results suggest that the proposed human interface is effective to adjust the stride length of a legged locomotor device.

We address a gait pattern generation on a legged locomotor device (WPAL: wearable power-assist locomotor) for paraplegics. In the gait movement with WPAL, a backward falling is a considerable problem, and a foot-floor collision during a swing movement would induce a loss of balance. In addition, adjustability of the gait parameters, such as stride length, gait cycle and maximum hight of the toe clearance, would be required for an individual paraplegic according to the degrees of his disabilities and skills. In this paper, we propose a gait pattern generation method considering the requirements of the stability and the adjustability. First, the trajectories of toe position, horizontal hip position, and foot plantar angle are calculated using a minimum jerk trajectory with the constraints of the position and velocity at via points. Second, the desired trajectories of joint angles are determined from the calculated trajectories by inverse kinematic equations. We demonstrate that generated desired trajectories for various gait parameter values and boundary conditions were satisfied with the required stability conditions.