Toe-off Motion Research Articles

Kid-size robot humanoid walking with heel-contact and toe-off motion.

Human-like features, like toe-off, heel-strike can enhance the performance of bipedal robots. However, few studies have considered the anthropomorphism of walking planning. Fewer studies have achieved their toe-off, heel-strike gait planning framework in a child-sized humanoid robot platform. This paper presents a human-like walking control framework based on the Divergent Component of Motion (DCM) com planning method that enables a child-sized humanoid robot to walk with a humanoid pattern with a speed of 0.6 s per step a strike of 30 cm. The control framework consists of three parts: the human-like gait generation of the center of mass (CoM) and swings foot trajectory, the dynamic replan in phase switch and the upper body stabilization controller. The dynamic replanning of the CoM and foot trajectory can efficiently decrease the vibration in the step-phase switch. The up-body stabilization controller can reduce the up-body swing in walking and increase the robot's stability while walking. The robot uses a mems-based inertial measurement unit (IMU) and joint position encoders to estimate the current state of the robot and use force-sensitive resistors (FSR) on the robot foot to identify the actual step phase of the robot. None of these solutions is high-cost or difficult to integrate with a child-size robot. Software simulations and walking experiments are using to verify the motion control algorithm. The effectiveness of the pattern generation and the controller can realize more human-like walking styles in a child-size robot are confirmed.

Heel-strike and toe-off motions optimization for humanoid robots equipped with active toe joints

SUMMARYIn this paper, a walking pattern optimization procedure is implemented to yield the optimal heel-strike and toe-off motions for different goal functions. To this end, first, a full dynamic model of a humanoid robot equipped with active toe joints is developed. This model consists of two parts: multi-body dynamics of the robot which is obtained by Lagrange and Kane methods and power transmission dynamic model which is developed using system identification approach. Then, a gait planning routine is presented and consistent parameters are specified. Several simulations and experimental tests are carried out on SURENA III humanoid robot which is designed and fabricated at the Center of Advanced Systems and Technologies located in the University of Tehran. Afterward, a genetic algorithm optimization is adopted to compute the optimal walking patterns for five different goal functions including energy consumption, stability margin, joint velocity, joint torque and required friction coefficient. Also, several parametric analyses are performed to characterize the effects of heel-strike and toe-off angle and toe link mass and length on these five goal functions. Finally, it is concluded that walking pattern without heel-strike and toe-off motions requires less friction coefficient than the pattern with heel-strike and toe-off motions. Also, heavier toe link lowers tip-over instability and slippage occurrence possibility, but requires more energy consumption and joint torque.

An Investigation on the Usefulness of Employing a Two-Segment Foot for Traversing Stairs

In this paper, effects of employing toe-off and heel-contact gait phases on the performance of bipedal robots traversing stairs are examined. The main goal is to demonstrate the hypothesis that employing toes and heels during walking up and down stairs improves the gait performance in terms of actuating joint torques and energy consumption. For this purpose, a comprehensive dynamics model for a 3D biped robot is developed and the inverse dynamics solutions during various walking phases are presented. To realize walking up and down stairs, a zero moment point (ZMP)-based pattern generation routine in the task space is proposed. In this routine, first, trajectories for the feet and the pelvis in the task space are designed to realize the desired task and preserve the feasibility constraints. Then, consistent with the topology of walking, suitable trajectory for the toe joint is generated. To examine the effects of heel-contact and toe-off gait phases, three walking topologies for walking up stairs and four walking topologies for walking down stairs, depending on the use of toe-off and heel-contact motions, are considered. For these topologies, the optimization procedure is conducted to yield the optimal patterns. Finally, the obtained patterns are compared in terms of energy consumption and joint torques, while obtained results show a significant improvement in the gait performance in terms of considered cost functions.

Analytical Dynamic Modelling of Heel-off and Toe-off Motions for a 2D Humanoid Robot

The main objective of this article is to optimize the walking pattern of a 2D humanoid robot with heel-off and toe-off motions in order to minimize the energy consumption and maximize the stability margin. To this end, at first, a gait planning method is introduced based on the ankle and hip joint position trajectories. Then, using these trajectories and the inverse kinematics, the position trajectories of the knee joint and all joint angles are determined. Afterwards, the dynamic model of the 2D humanoid robot is derived using Lagrange and Kane methods. The dynamic model equations are obtained for different phases of motion and the unknowns, including ground reactions, and joint torques are also calculated. Next, the derived dynamic model is verified by comparing the position of the ZMP point based on the robot kinematics and the ground reactions. Then, the obtained trajectories have been optimized to determine the optimal heel-off and toe-off angles using a genetic algorithm (GA) by two different objective functions: minimum energy consumption and maximum stability margin. After optimization, a parametric analysis has been adopted to inspect the effects of heel-off and toe-off motions on the selected objective functions. Finally, it is concluded that to have more stable walking in high velocities, small angles of heel-off and toe-off motions are needed. Consequently, in low velocities, walking patterns with large angles of heel-off and toe-off motions are more stable. On the contrary, large heel-off and toe-off motions lead to less energy consumption in high velocities, while small heel-off and toe-off motions are suitable for low velocities. Another important point is that for the maximum stability optimization, compared to minimum energy consumption optimization, more heel-off and toe-off motions are needed.

Three-Dimensional Bipedal Walking Control Based on Divergent Component of Motion

In this paper, the concept of divergent component of motion (DCM, also called “Capture Point”) is extended to 3-D. We introduce the “Enhanced Centroidal Moment Pivot point” (eCMP) and the “Virtual Repellent Point” (VRP), which allow for the encoding of both direction and magnitude of the external forces and the total force (i.e., external plus gravitational forces) acting on the robot. Based on eCMP, VRP, and DCM, we present methods for real-time planning and tracking control of DCM trajectories in 3-D. The basic DCM trajectory generator is extended to produce continuous leg force profiles and to facilitate the use of toe-off motion during double support. The robustness of the proposed control framework is thoroughly examined, and its capabilities are verified both in simulations and experiments.

Foot Placement Modification for a Biped Humanoid Robot with Narrow Feet

This paper describes a walking stabilization control for a biped humanoid robot with narrow feet. Most humanoid robots have larger feet than human beings to maintain their stability during walking. If robot's feet are as narrow as humans, it is difficult to realize a stable walk by using conventional stabilization controls. The proposed control modifies a foot placement according to the robot's attitude angle. If a robot tends to fall down, a foot angle is modified about the roll axis so that a swing foot contacts the ground horizontally. And a foot-landing point is also changed laterally to inhibit the robot from falling to the outside. To reduce a foot-landing impact, a virtual compliance control is applied to the vertical axis and the roll and pitch axes of the foot. Verification of the proposed method is conducted through experiments with a biped humanoid robot WABIAN-2R. WABIAN-2R realized a knee-bended walking with 30 mm breadth feet. Moreover, WABIAN-2R mounted on a human-like foot mechanism mimicking a human's foot arch structure realized a stable walking with the knee-stretched, heel-contact, and toe-off motion.

Emulation of Human Walking by Biped Humanoid Robot with Heel-Contact and Toe-Off Motion

The foot mechanism and pattern generation we propose for a biped humanoid robot achieves human-like heel-contact toe-off walking. Placing its heel and toes simultaneously on the ground while walking makes it difficult for a robot to take long strides and mimic human gaits. To solve this problem, we developed a biped foot with one passive toe joint based on human gaits analyzed by motion capture and propose pattern generation for human-like walking based on the zero moment point (ZMP) criterion. Using a genetic algorithm, we optimize walking parameters to generate continuous, smooth foot trajectories. Results of experiments in heel-contact toe-off walking in ground reaction force (GRF) using the biped humanoid robot WABIAN-2 demonstrated the similarity between proposed and human walking.

2足歩行ロボットにおける片脚支持期の重心速度変動幅最小化のための目標ZMP軌道

The referential ZMP (Zero-Moment Point) trajectory that minimizes the variation of COG (Center of Gravity) velocity in the single support phase of a biped robot is shown. Two advantages of using this ZMP trajectory are discussed. The first advantage is that the variation of COG velocity is gradual. The second advantage is that the biped robot enables the heel-contact motion and the toe-off motion in the single support phase. The trajectory planning based on this ZMP trajectory is proposed. In simulation and experiment, the validity of the proposed method was confirmed.

2A1-D19 踵接地・爪先離地動作に着目したヒューマノイドロボットのヒト歩行模擬

A humanoid robot -WABIAN-2R- capable of human-like walks with knees stretched, heel-contact and toe-off motion is proposed in this paper. WABIAN-2R has two 1-DOF passive joint in its feet to bend toes in steady walking. Also it has two 6-DOF legs, a 2-DOF pelvis, a 2-DOF trunk, two 7-DOF arms with 3-DOF hands, and a 3-DOF neck. Furthermore a new pattern generation algorithm for walking patterns with knee stretched, heel-contact and toe-off motion based on ZMP criterion is described. In this pattern generation, some parameters of foot trajectories of a biped robot are optimized by using a Genetic Algorithm in order to generate a continuous and smooth leg motion. Software simulations and walking experiments are conducted, and the effectiveness of the pattern generation and mechanism of WABIAN-2R that have an ability to realize more human-like walking styles of a humanoid robot. is confirmed.

Control of the heel-off to toe-off motion of a dynamic biped gait

A mechanism for the control of the heel-off to toe-off motion of a dynamic biped gait is presented. It is argued that the reaction force between the ground and the biped foot is an important factor in a satisfactory implementation of dynamic gait. This force must be properly controlled while the foot is in the heel-off to toe-off phase. Since the foot rolls over the ground surface in this phase and the global description of the surface is unknown, the foot has to execute a nonholonomic constraint motion. The formulations of nonholonomic constraints and system dynamics under the constraints are derived for the roll-over motion. A feedback control mechanism is designed based on the formulations. The formulation and the feedback control mechanism are applied to a four-link biped model. Successful simulation results of the heel-off to toe-off motion prove that the formulation and control mechanism are valid for the nonholonomically constrained motion of the biped. >