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.

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.

This paper presents an effective method for planning and optimizing robot motions in joint space using via-points. The via-point formulation allows for a sparse movement representation which is inherently smooth according to a minimum jerk criterion. In this research we focus on two aspects. First, we present an initialization method to find a feasible number of via-points and their distribution in time. This initialization takes the difficulty of the planning problem into account and finds a tradeoff between representation complexity (number of via-points) and optimization time. Second, we propose a two-step optimization approach to improve the via-point parameters to satisfy constraints over the whole motion duration. We show that our methods generate feasible and smooth robot motions with a high success rate for tasks of varying complexity. The methods are evaluated in simulation using four different scenarios with two different robots, a 7-DOF robot arm and a 16-DOF humanoid upper body. Additionally, the experiments with the robot arm are shown in a real-world experiment.

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.

Parametric excitation walking is one of methods to realize dynamic walking on a level ground. This method has first applied to a biped robot with telescopic legs and later to a robot with actuated knee joints. In parametric excitation walking, mechanical energy is increased by periodic up-and-down motion of the center of mass. While parametric excitation walking with telescopic legs has verified by an experimental robot, that with actuated knees has not yet as far as we know. The purpose of this paper is to present demonstration experiment of parametric excitation walking with a kneed biped robot. To do this, we develop an experimental kneed biped robot having four parallel legs with semicircular feet. In the experiment, the robot achieves walking on a level ground more than 15 steps. We also measure the movements of the robot during walking by a 3D motion capture and compare with simulation results.

Parametric excitation walking is one of methods that realize a passive dynamic like walking on the level ground. In parametric excitation walking, up-and-down motion of the center of mass restores mechanical energy and sustainable gait is generated. Walking ability and walking performance strongly depend on the reference trajectory of the center of mass. In this paper, we propose an optimization method for the reference trajectory of parametric excitation walking. There are two problems for optimization. One is that search space of a reference trajectory is inherently infinite dimensional. Another is that it takes long simulation time to generate steady gait for a given reference trajectory. Therefore, the proposing optimization method adopts the following strategy. For the former, we confine the reference trajectory to the quartic spline curve and take the parameter of spline curve as decision variables. For the latter, we discretize the search space and adopt a local search method usually used in combinational optimization problems. We apply the proposed method to a kneed biped robot, and optimize the reference trajectory of its swing leg.

In the passive dynamic walking proposed by McGeer, mechanical energy lost by heel strike is restored by transporting potential energy to kinetic energy as walking down a slope. When energy input is large such as an angle of slope is steep, bifurcation of walking period occurs. In parametric excitation walking, which is one method to realize passive dynamic-like walking on level ground, bifurcation has also been observed when walking speed is fast. Asano et al. have shown that bifurcation exerts an adverse influence upon walking performance by using rimless wheel model. In this paper, we apply delayed feedback control (DFC) originally used in chaos control to parametric excitation walking to suppress bifurcation. We show in numerical simulation that the proposed method makes two-period walking to one-period walking, and energy efficiency is improved. The analyses using Poincare¿ map reveal that the one-period walking with DFC is unstable periodic orbit and that the robot dealt in this paper satisfies the sufficient condition of applicability of DFC.

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.

The parametric excitation based gait generation method proposed by Asano et al. restores mechanical energy lost by heel-strike collisions. Harata et. al. applied this method to a kneed biped robot which is proper for the parametric excitation, and show that sustainable gait has been generated with only knee torque. A swing-leg of a kneed biped robot has similar mechanism to an acrobot, and many acrobots bends a joint in inverse direction like ornithoid walking. This suggests that inverse bending a knee restores more mechanical energy than forward bending like human walking, and hence, inverse bending may be more efficient. In this paper, we propose a parametric excitation based ornithoid gait generation method for a kneed biped robot, and show that it can walk sustainably by numerical simulation. We also show that parametric excitation based inverse bending walking is more efficient than parametric excitation based forward bending walking with respect to performance indices in our model.

This paper presents a learning approach to acquisition of manipulation control for carrying an object accompanied with stick/slip mode switchings. The proposed learning architecture has hierarchical structure. The upper layer determines a global trajectory and a sequence of mode switchings by reinforcement learning while giving the lower layer commands about small motions keeping (sliding or sticking) modes. The lower layer realizes a desired small regional motion using the estimated boundary information about mode switches by support vector machine (SVM). Mode transition data are collected off-line for SVM learning. The proposed learning framework is applied to an object moving task with two-DOF manipulator, where the desired configuration of the object is specified so that stick/slip mode switchings are inevitable to accomplish the given task. Simulation showed that the proposed learning architecture realized an object control with stick/slip mode switching.

It is hypothesized that suitable forces and postures of digits for holding an object are planned simultaneously based on the same motor criterion, using an internal representation of the object. To demonstrate the computational potential of this hypothesis, a neural network model for learning and planning forces and postures of digits in object holding tasks is proposed. Integrating visual 2D images of 9 objects that are different in size and orientation with forces and postures of digits, the neural network internally represents the size and the orientation of the objects and memorizes 5 motor patterns per object. Moreover, the neural network restores forces and postures in natural holding tasks according to the same motor strategy in which a norm of forces of digits is minimized. These results support the computational plausibility of our hypothesis.

Restoring mechanical energy lost by heel-strike collisions is necessary for stable gait generation. One principle to realize this is parametric excitation. Recently, Asano et al. applied this principle to a biped robot with telescopic-legs, and succeeded in generating a sustainable biped gait by computer simulation. In this paper, we deal with a model of a biped robot that has not only semicircular feet but also actuated knees. Though this robot has no actuator at the hip, knee actuators can sustain gait by parametric excitation. We first verify that an actuated knee can cause parametric excitation, and then show by computer simulation that the proposed biped robot can walk continuously with actuated knees only.