Generation of bipedal walking through interactions among the robot dynamics,the oscillator dynamics,and the environment: Stability characteristics of a five-link planar biped robot

We previously developed a locomotion control system for a biped robot using nonlinear oscillators and verified the performance of this system in order to establish adaptive walking through the interactions among the robot dynamics, the oscillator dynamics, and the environment. In order to clarify these mechanisms, we investigate the stability characteristics of walking using a five-link planar biped robot with a torso and knee joints that has an internal oscillator with a stable limit cycle to generate the joint motions. Herein we conduct numerical simulations and a stability analysis, where we analytically obtain approximate periodic solutions and examine local stability using a Poincaré map. These analyses reveal (1) stability characteristics due to locomotion speed, torso, and knee motion, (2) stability improvement due to the modulation of oscillator states based on phase resetting using foot-contact information, and (3) the optimal parameter in the oscillator dynamics for adequately exploiting the interactions among the robot dynamics, the oscillator dynamics, and the environment in order to increase walking stability. The results of the present study demonstrate the advantage and usefulness of locomotion control using oscillators through mutual interactions.     

Optimization and evaluation of swing leg retraction for a hydraulic biped robot

To improve the locomotion performance of legged robots, the swing leg retraction (SLR) technique is investigated in a hydraulic biped robot. First, the influence of SLR on the locomotion performance of the hydraulic biped robot is analyzed in theory and simulations based on an extended spring load inverted pendulum model. The influence contains three performance indicators: energy loss/effiency, friction/slipping, and impact/compliance. Second, by synthesizing three performance indicators, using unified objective method and particle swarm optimization algorithm, the optimal SLR rate for gait planning based on Bezier curve is addressed. Finally, experiments are implemented to validate the effectiveness and feasibility of proposed method. And, the results show that the SLR technique is useful to reduce the impact force, improve the robot's locomotion stability and make room for impedance performance improvement of compliance controller. This research provides an insight for locomotion control of hydraulic legged robots.     

正弦驱动与传感反馈结合的双足机器人仿生行走控制

提出了一种正弦驱动与传感反馈结合的双足机器人仿生行走控制方法．所有关节由正弦振荡器驱动, 较之相互耦合的神经元振荡器更加简单;控制参数具有明晰的物理意义,便于对运动模式进行调节．传感反馈表征 了机器人的运动状态,对于保证机器人的稳定行走起着至关重要的作用．将机器人碰地、碰膝等关键运动状态作为 相位反馈,对控制力矩进行相位重置,协调各关节动作,进而实现控制器、机器人、环境的耦合．同时,从节省能量 和仿生的角度,考虑了关节运动的被动特性,确定了各关节力矩的作用区间．仿真结果表明,该控制方法能实现机 器人稳定行走,并具有良好的能效性和自稳定性.     

Demonstration and Analysis of Quadrupedal Passive Dynamic Walking

Animals, including human beings, can travel in a variety of environments adaptively. Legged locomotion makes this possible. However, legged locomotion is temporarily unstable and finding out the principle of walking is an important matter for optimum locomotion strategy or engineering applications. As one of the challenges, passive dynamic walking has been studied on this. Passive dynamic walking is a walking phenomenon in which a biped walking robot with no actuator walks down a gentle slope. The gait is very smooth (like a human) and much research has been conducted on this. Passive dynamic walking is mainly about bipedalism. Considering that there are more quadruped animals than bipeds and a four-legged robot is easier to control than a two-legged robot, quadrupedal passive dynamic walking must exist. Based on the above, we studied saggital plane quadrupedal passive dynamic walking simulation. However, it was not enough to attribute the result to the existence of quadrupedal passive dynamic walking. In this research, quadrupedal passive dynamic walking is experimentally demonstrated by the four-legged walking robot 'Quartet 4'. Furthermore, changing the type of body joint, slope angle, leg length and variety of gaits (characteristics in four-legged animals) was observed passively. Experimental data could not have enough walking time and could not change parameters continuously. Then, each gait was analyzed quantitatively by the experiment and three-dimensional simulation.     

动态双足机器人的控制与优化研究进展

对动态双足机器人的可控周期步态的稳定性、鲁棒性和优化控制策略的国内外研究现状与发展趋势进行了探讨.首先,介绍动态双足机器人的动力学数学模型,进一步,提出动态双足机器人运动步态和控制系统原理;其次,讨论动态双足机器人可控周期步态稳定性现有的研究方法,分析这些方法中存在的缺点与不足;再次,研究动态双足机器人的可控周期步态优化控制策略,阐明各种策略的优缺点;最后,给出动态双足机器人研究领域的难点问题和未来工作,展望动态双足机器人可控周期步态与鲁棒稳定性及其应用的研究思路.     

Near Optimal PID Controllers for the Biped Robot While Walking on Uneven Terrains

The execution of the gaits generated with the help of a gait planner is a crucial task in biped locomotion. This task is to be achieved with the help of a suitable torque based controller to ensure smooth walk of the biped robot. It is important to note that the success of the developed proportion integration differentiation (PID) controller depends on the selected gains of the controller. In the present study, an attempt is made to tune the gains of the PID controller for the biped robot ascending and descending the stair case and sloping surface with the help of two non-traditional optimization algorithms, namely modified chaotic invasive weed optimization (MCIWO) and particle swarm optimization (PSO) algorithms. Once the optimal PID controllers are developed, a simulation study has been conducted in computer for obtaining the optimal tuning parameters of the controller of the biped robot. Finally, the optimal gait angles obtained by using the best controller are fed to the real biped robot and found that the biped robot has successfully negotiated the said terrains.     

Minimalistic control of biped walking in rough terrain

Toward our comprehensive understanding of legged locomotion in animals and machines, the compass gait model has been intensively studied for a systematic investigation of complex biped locomotion dynamics. While most of the previous studies focused only on the locomotion on flat surfaces, in this article, we tackle with the problem of bipedal locomotion in rough terrains by using a minimalistic control architecture for the compass gait walking model. This controller utilizes an open-loop sinusoidal oscillation of hip motor, which induces basic walking stability without sensory feedback. A set of simulation analyses show that the underlying mechanism lies in the “phase locking” mechanism that compensates phase delays between mechanical dynamics and the open-loop motor oscillation resulting in a relatively large basin of attraction in dynamic bipedal walking. By exploiting this mechanism, we also explain how the basin of attraction can be controlled by manipulating the parameters of oscillator not only on a flat terrain but also in various inclined slopes. Based on the simulation analysis, the proposed controller is implemented in a real-world robotic platform to confirm the plausibility of the approach. In addition, by using these basic principles of self-stability and gait variability, we demonstrate how the proposed controller can be extended with a simple sensory feedback such that the robot is able to control gait patterns autonomously for traversing a rough terrain.     

Dynamic turning control of a quadruped locomotion robot using oscillators

We propose a dynamic turning control system for a quadruped robot that uses non-linear oscillators. It is composed of a spontaneous locomotion controller and voluntary motion controller. We verified the mechanical capabilities of the dynamic turning motion of the proposed control system through numerical simulations and hardware experiments. Various turning speeds and orientations made the motion of the robot asymmetrical in terms of the duty ratio, stride and center of pressure. The proposed controller actively and adaptively controlled redundant degrees of freedom to cancel out dynamic asymmetry, and established stable turning motion at various locomotion speeds and turning orientations.     

基于GCIPM行走的步行机器人路径规划

介绍了利用重力补偿倒立摆方式（GCIPM）提高步行机器人行走的稳定性。该方法与以往利用线性倒立摆方式（IPM）控制的机器人相似,但是考虑了期望轨迹上机器人的迈步腿力。当基于IPM的路径规划应用到实际的步行机器人上,依据ZMP控制理论从预固定点移动时,被忽略的迈步腿力的变化在实际中使稳定性得不到保证。由于GCIPM考虑了迈步腿力的影响,仿真表明,应用GCIPM的步行机器人,稳定性得到优化提高。     

基于主—从控制的双足机器人动步态行走

本文给出一种基于主-从控制实现双足机器人动步态行走的控制方法.该方法计算量小,可以在线规划步态及实现双脚支撑期平滑的动态切换.仿真及实验结果验证了方法的有效性及可行性,实现了变步态动态行走.实验所采用的装置为 HLTR—13双足机器人.该机器人重65kg,高1.1m,具有12个自由度.实验结果表明,本文给出的方法能较好地实现变步态动态行走。从而使机器人具有较强的环境适应能力.     

Position-based impedance control of a biped humanoid robot

This paper describes position-based impedance control for biped humanoid robot locomotion. The impedance parameters of the biped leg are adjusted in real-time according to the gait phase. In order to reduce the impact/contact forces generated between the contacting foot and the ground, the damping coefficient of the impedance of the landing foot is increased largely during the first half double support phase. In the last half double support phase, the walking pattern of the leg changed by the impedance control is returned to the desired walking pattern by using a polynomial. Also, the large stiffness of the landing leg is given to increase the momentum reduced by the viscosity of the landing leg in the first half single support phase. For the stability of the biped humanoid robot, a balance control that compensates for moments generated by the biped locomotion is employed during a whole walking cycle. For the confirmation of the impedance and balance control, we have developed a life-sized humanoid robot, WABIAN-RIII, which has 43 mechanical d.o.f. Through dynamic walking experiments, the validity of the proposed controls is verified.     

Adaptive Robot Biped Locomotion with Dynamic Motion Primitives and Coupled Phase Oscillators

In order to properly function in real-world environments, the gait of a humanoid robot must be able to adapt to new situations as well as to deal with unexpected perturbations. A promising research direction is the modular generation of movements that results from the combination of a set of basic primitives. In this paper, we present a robot control framework that provides adaptive biped locomotion by combining the modulation of dynamic movement primitives (DMPs) with rhythm and phase coordination. The first objective is to explore the use of rhythmic movement primitives for generating biped locomotion from human demonstrations. The second objective is to evaluate how the proposed framework can be used to generalize and adapt the human demonstrations by adjusting a few open control parameters of the learned model. This paper contributes with a particular view into the problem of adaptive locomotion by addressing three aspects that, in the specific context of biped robots, have not received much attention. First, the demonstrations examples are extracted from human gaits in which the human stance foot will be constrained to remain in flat contact with the ground, forcing the “bent-knee” at all times in contrast with the typical straight-legged style. Second, this paper addresses the important concept of generalization from a single demonstration. Third, a clear departure is assumed from the classical control that forces the robot’s motion to follow a predefined fixed timing into a more event-based controller. The applicability of the proposed control architecture is demonstrated by numerical simulations, focusing on the adaptation of the robot’s gait pattern to irregularities on the ground surface, stepping over obstacles and, at the same time, on the tolerance to external disturbances.     

Adaptive splitbelt treadmill walking of a biped robot using nonlinear oscillators with phase resetting

To investigate the adaptability of a biped robot controlled by nonlinear oscillators with phase resetting based on central pattern generators, we examined the walking behavior of a biped robot on a splitbelt treadmill that has two parallel belts controlled independently. In an experiment, we demonstrated the dynamic interactions among the robot mechanical system, the oscillator control system, and the environment. The robot produced stable walking on the splitbelt treadmill at various belt speeds without changing the control strategy and parameters, despite a large discrepancy between the belt speeds. This is due to modulation of the locomotor rhythm and its phase through the phase resetting mechanism, which induces the relative phase between leg movements to shift from antiphase, and causes the duty factors to be autonomously modulated depending on the speed discrepancy between the belts. Such shifts of the relative phase and modulations of the duty factors are observed during human splitbelt treadmill walking. Clarifying the mechanisms producing such adaptive splitbelt treadmill walking will lead to a better understanding of the phase resetting mechanism in the generation of adaptive locomotion in biological systems and consequently to a guiding principle for designing control systems for legged robots.     

Locomotion Control of a Biped Robot Using Nonlinear Oscillators

Recently, many experiments and analyses with biped robots have been carried out. Steady walking of a biped robot implies a stable limit cycle in the state space of the robot. In the design of a locomotion control system, there are primarily three problems associated with achieving such a stable limit cycle: the design of the motion of each limb, interlimb coordination, and posture control. In addition to these problems, when environmental conditions change or disturbances are added to the robot, there is the added problem of obtaining robust walking against them. In this paper we attempt to solve these problems and propose a locomotion control system for a biped robot to achieve robust walking by the robot using nonlinear oscillators, each of which has a stable limit cycle. The nominal trajectories of each limb's joints are designed by the phases of the oscillators, and the interlimb coordination is designed by the phase relation between the oscillators. The phases of the oscillators are reset and the nominal trajectories are modified using sensory feedbacks that depend on the posture and motion of the robot to achieve stable and robust walking. We verify the effectiveness of the proposed locomotion control system, analyzing the dynamic properties of the walking motion by numerical simulations and hardware experiments. Shinya Aoi received the B.E. and M.E. degrees from the Department of Aeronautics and Astronautics, Kyoto University, Kyoto, Japan in 2001 and 2003, respectively. He is a Ph.D. candidate in the Department of Aeronautics and Astronautics, Kyoto University. Since 2003, he has been a research fellow of the Japan Society for the Promotion of Science (JSPS). His research interests include dynamics and control of robotic systems, especially legged robots. He is a member of IEEE, SICE, and RSJ. Kazuo Tsuchiya received the B.S., M.S., and Ph.D. degrees in engineering from Kyoto University, Kyoto, Japan in 1966, 1968, and 1975, respectively. From 1968 to 1990, he was a research member of Central Research Laboratory in Mitsubishi Electric Corporation, Amagasaki, Japan. From 1990 to 1995, he was a professor at the Department of Computer Controlled Machinery, Osaka University, Osaka, Japan. Since 1995, he has been a professor at the Department of Aeronautics and Astronautics, Kyoto University. His fields of research include dynamic analysis, guidance, and control of space vehicles, and nonlinear system theory for distributed autonomous systems. He is currently the principal investigator of “Research and Education on Complex Functional Mechanical Systems” under the 21st Century Center of Excellence Program (COE program of the Ministry of Education, Culture, Sports, Science and Technology, Japan).     

Toward the enhancement of biped locomotion and control techniques: walking pattern classification

A new walking pattern classification method is proposed for a 5-link 7-DOF biped robot walking on an uneven floor. This method extracts the patterns in the current floor position of the stance foot and the transitioning floor conditions of the swing foot during locomotion. When a global path composed of stairs, obstacles, etc., and certain walking parameters, such as the speed of walking and the total walking time, are put into the system, the guidance controller unit determines the trajectory of the footsteps in terms of step patterns by using a genetic algorithm-based optimization technique while ensuring the biped’s stability criterion. A demonstration of the biped with different pattern classes was realized by a dynamic simulator.     

Overview of the Lucy Project: Dynamic Stabilization of a Biped Powered by Pneumatic Artificial Muscles

This paper gives an overview of the Lucy project. What is special is that the biped is not actuated with the classical electrical drives, but with pleated pneumatic artificial muscles. In an antagonistic setup of such muscles both the torque and the compliance are controllable. From human walking there is evidence that joint compliance plays an important role in energy-efficient walking and running. To be able to walk at different walking speeds and step lengths, a trajectory generator and joint trajectory tracking controller are combined. The first generates dynamically stable trajectories based on the objective locomotion parameters which can be changed from step to step. The joint trajectory tracking unit controls the pressure inside the muscles so the desired motion is followed. It is based on a computed torque model and takes the torque–angle relation of the antagonistic muscle setup into account. With this strategy the robot is able to walk at a speed up to 0.15 m/s. A compliance controller is developed to reduce the energy consumption by combining active trajectory control with the exploitation of the natural dynamics. A mathematical formulation was developed to find an optimal compliance setting depending on the desired trajectory and physical properties of the system. This strategy is experimentally evaluated on a single pendulum structure and not implemented on the real robot because the walking speed of the robot is currently too slow. At the end a discussion is given about the pros and cons of building a pneumatic biped, and the control architecture used.     

基于深度强化学习的双足机器人斜坡步态控制方法

为提高准被动双足机器人斜坡步行稳定性, 本文提出了一种基于深度强化学习的准被动双足机器人步态控制方法. 通过分析准被动双足机器人的混合动力学模型与稳定行走过程, 建立了状态空间、动作空间、episode过程与奖励函数. 在利用基于DDPG改进的Ape-X DPG算法持续学习后, 准被动双足机器人能在较大斜坡范围内实现稳定行走. 仿真实验表明, Ape-X DPG无论是学习能力还是收敛速度均优于基于PER的DDPG. 同时, 相较于能量成型控制, 使用Ape-X DPG的准被动双足机器人步态收敛更迅速、步态收敛域更大, 证明Ape-X DPG可有效提高准被动双足机器人的步行稳定性.     

Controlled passive dynamic running experiments with the ARL-monopod II

This paper presents the expansion and implementation of the controlled passive dynamic running (CPDR) strategy for legged robots, previously presented by the authors. The CPDR exploits the underlying passive dynamic operation of the robot's mechanical systems to reduce the energy spent for locomotion. Meanwhile, it ensures the stability of the vertical and forward motions as the robot speed varies. An "adaptive energy controller" stabilizes the hopping height accurately over a range of operating conditions. The passive dynamic derivations for the Monopod, together with the foot-placement algorithm and model-based joint controllers, are used to control the forward speed about the passive operation trajectories. New locomotion variables are used for robust synchronization between the hip-body and the leg oscillations. ARL-Monopod II achieved a speed of 1.25 m/s with specific resistance (a measure for energy cost of locomotion) of 30% of the earlier robot ARL-Monopod I, its predecessor, due to the newer hip and leg design and application of the CPDR control strategy.     

Robust Sliding-mode Control of Nine-link Biped Robot Walking

A nine-link planar biped robot model is considered which, in addition tothe main links (i.e., legs, thighs and trunk), includes a two-segment foot.First, a continuous walking pattern of the biped on a flat terrain issynthesized, and the corresponding desired trajectories of the robot jointsare calculated. Next, the kinematic and dynamic equations that describe itslocomotion during the various walking phases are briefly presented. Finally,a nonlinear robust control approach is followed, motivated by the fact thatthe control which has to guarantee the stability of the biped robot musttake into account its exact nonlinear dynamics. However, an accurate modelof the biped robot is not available in practice, due to the existence ofuncertainties of various kinds such as unmodeled dynamics and parameterinaccuracies. Therefore, under the assumption that the estimation error onthe unknown (probably time-varying) parameters is bounded by a givenfunction, a sliding-mode controller is applied, which provides a successfulway to preserve stability and achieve good performance, despite the presenceof strong modeling imprecisions or uncertainties. The paper includes a setof representative simulation results that demonstrate the very good behaviorof the sliding-mode robust biped controller.