Gait generation and control for biped robots with underactuation degree one

The paper develops a unified feedback control law for n degree-of-freedom biped robots with one degree of underactuation so as to generate periodic orbits on different slopes. The periodic orbits on different slopes are produced from an original periodic orbit, which is either a natural passive limit cycle on a specific slope or a stable periodic walking gait on level ground generated with active control. First, inspired by the controlled symmetries approach, a general result on gait generation on different slopes based on a periodic orbit on a specific slope is obtained. Second, the time-scaling control approach is integrated to reproduce geometrically same periodic orbits for biped robots with one degree of underactuation. The degree of underactuation is compensated by one degree-of-freedom in the temporal evolution that scales the original periodic orbit. Necessary and sufficient conditions are investigated for the existence and stability properties of periodic orbits on different slopes with the proposed control law. Finally, the proposed approach is illustrated by two kinds of underactuated biped robots: one has a passive gait on a specific ground slope and the other does not have a natural passive gait.     

Passive dynamic turning in 3D biped locomotion: an extension to passive dynamic walking

Passive dynamic walking usually refers to a kind of walking where a biped walker is able to walk downhill, without any actuation or control, just due to the gravity. Although most of works done in this regard have concentrated on passive walking along a straight line, in this paper we extend this concept to a more general case of locomotion, i.e. turning or walking along curved path. We call the novel extension passive turning, and categorize it to two types of finite and infinite. We showed that the finite type is still applicable on a typical downhill or ramp, while the infinite type is only practical on a specific surface profile that we call it helical ramp. Furthermore, several stability and parameter analysis are also conducted to evaluate more aspects of this notion. We highlighted that surprisingly, the passive straight walking is actually a special case of passive turning, just with infinite radius of turn and less asymptotical stability. It should be noted that the present study is performed using a model of an arc-foot three-dimensional (3D) compass gait walker.     

Stability and control of dynamic walking for a five-link planar biped robot with feet

During dynamic walking of biped robots, the underactuated rotating degree of freedom （DOF） emerges between the support foot and the ground, which makes the biped model hybrid and dimension-variant. This paper addresses the asymptotic orbit stability for dimension-variant hybrid systems （DVHS）. Based on the generalized Poincare map, the stability criterion for DVHS is also presented, and the result is then used to study dynamic walking for a five-link planar biped robot with feet. Time-invariant gait planning and nonlinear control strategy for dynamic walking with fiat feet is also introduced. Simulation results indicate that an asymptotically stable limit cycle of dynamic walking is achieved by the proposed method.     

Central pattern generators based on Matsuoka oscillators for the locomotion of biped robots

Biologically inspired control approaches based on central pattern generators (CPGs) with neural oscillators have been drawing much attention for the purpose of generating rhythmic motion for biped robots with human-like locomotion. This article describes the design of a neural-oscillator-based gait-rhythm generator using a network of Matsuoka oscillators to generate a walking pattern for biped robots. This includes the proper consideration of the oscillator’s parameters, such as a time constant for the adaptation rate, coupling factors for mutual inhibitory connections, etc., to obtain a stable and desirable response from the network. The article examines the characteristics of a CPG network with six oscillators, and the effect of assigning symmetrical and asymmetrical coupling coefficients among oscillators within the network structure under different possible inhibitions and excitations. The kinematics and dynamics of a five-link biped robot have been modeled, and its joints are actuated through simulation by the torques output from the neural rhythm generator to generate the trajectories for hip, knee, and ankle joints. The parameters of the neural oscillators are tuned to achieve flexible trajectories. The CPG-based control strategy is implemented and tested through a simulation. This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007     

A hybrid SOF-PID controller for a MIMO biped robot

The application of the hybrid self-organizing fuzzy (SOF) PID controller to a multiinput multioutput nonlinear biped robot is studied in this article. The SOF-PID controller was initially studied by H.B. Kazemian in 1998. Actually, his SOF-PID controller has limits. The supervisory capacity of the SOF-PID controller can adjust only certain kinds of parameters. Here the hybrid SOF-PID controller is introduced to tune some kinds of parameters, and it was tested on a MIMO biped robot. In the experiment, the hybrid SOF-PID controller shows a better performance than the SOF-PID. This work was presented in part at the 10th International Symposium on Artificial Life and Robotics, Oita, Japan, February 4–6, 2005     

Imitation learning of humanoid locomotion using the direction of landing foot

Since it is quite difficult to create motions for humanoid robots having a fairly large number of degrees of freedom, it would be very convenient indeed if robots could observe and imitate what they want to create. To this end, this paper discusses how humanoid robots can learn through imitation taking into consideration the fact that demonstrator and imitator robots may have different kinematics and dynamics. As part of a wider interest in humanoid motion generation in general, this work mainly investigates how imitator robots adapt a reference locomotion gait copied from a demonstrator robot. Specifically, the self-adjusting adaptor is proposed, where the perceived locomotion pattern is modified to keep the direction of the lower leg contacting the ground identical between the demonstrator and the imitator, and to sustain dynamic stability by controlling the position of the center of mass. The validity of the proposed scheme is verified through simulations on OpenHRP and real experiments. Recommended by Editorial Board member Hyoukryeol Choi under the direction of Editor Jae-Bok Song. This work was conducted as a program for the “Fostering Talent in Emergent Research Fields” in Special Coordination Funds for the Promotion of Science and Technology by the Ministry of Education, Culture, Sports, Science and Technology of Japan. This work was also supported in part by MIC and IITA of Korea through IT Leading R&D Support Project. [2009-S028-01, Development of Cooperative Network-based Humanoids Technology] Woosung Yang received his B.S. and M.S. degrees in Mechanical Engineering from Sogang University, Seoul, Korea in 2001 and 2003, and his Ph.D. degree in the School of Information Science from Japan Advanced Institute of Science and Technology (JAIST), Ishikawa, Japan in 2007, respectively. Since 2007, he has been a Post-doctoral Researcher in Center for Cognitive Robotics, Korea Institute of Science and Technology. His research interests include intelligent control theory, biologically inspired control and system, humanoids, and actuator controls for small form factor precision devices. Nak Young Chong received his B.S., M.S., and Ph.D. in Mechanical Engineering from Hanyang University, Seoul, Korea in 1987, 1989, and 1994, respectively. He was senior researcher at Daewoo Heavy Industries Ltd. (1994–98), visiting researcher at MEL in Tsukuba, Japan (1995–96), and postdoctoral researcher at KIST (1998). From 1998–2007, he was on the research staff of AIST in Tsukuba, Japan. In 2003, he joined the faculty of JAIST as Associate Professor of Information Science. Dr. Chong served as Co-chair of the IEEE RAS Technical Committee on Networked Robots (2004–06), and the Fujitsu Scientific Systems Robotics WG (2004–06) and Robot Information Processing WG (2006–08), respectively. He visited Northwestern University (2001) and Georgia Tech (2008–09). He is currently serving as Associate Editor of the IEEE Transactions on Robotics and the International Journal of Assistive Robotics and Systems. He is the Korea Robotics Society director of international cooperation, and a member of IEEE, RSJ, and SICE.     

Optimal two-degree-of-freedom fuzzy control for locomotion control of a hydraulically actuated hexapod robot

Locomotion control of legged robots is a very challenging task because very accurate foot trajectory tracking control is necessary for stable walking. An electro-hydraulically actuated walking robot has sufficient power to walk on rough terrain and carry a heavier payload. However, electro-hydraulic servo systems suffer from various shortcomings such as a high degree of nonlinearity, uncertainty due to changing hydraulic properties, delay due to oil flow and dead-zone of the proportional electromagnetic control valves. These shortcomings lead to inaccurate analytical system model, therefore, application of classical control techniques result into large tracking error. Fuzzy logic is capable of modeling mathematically complex or ill-defined systems. Therefore, fuzzy logic is becoming popular for synthesis of control systems for complex and nonlinear plants. In this investigation, a two-degree-of-freedom fuzzy controller, consisting of a one-step-ahead fuzzy prefilter in the feed-forward loop and a PI-like fuzzy controller in the feedback loop, has been proposed for foot trajectory tracking control of a hydraulically actuated hexapod robot. The fuzzy prefilter has been designed by a genetic algorithm (GA) based optimization. The prefilter overcomes the flattery delay caused by the hydraulic dead-zone of the electromagnetic proportional control valve and thus helps to achieve better tracking. The feedback fuzzy controller ensures the stability of the overall system in the face of model uncertainty associated with hydraulically actuated robotic mechanisms. Experimental results exhibit that the proposed controller manifests better foot trajectory tracking performance compared to single-degree-of-freedom (SDF) fuzzy controller or optimal classical controller like state feedback LQR controller.     

Neuro-fuzzy gait synthesis with reinforcement learning for a biped walking robot

 A reinforcement learning-based neuro-fuzzy gait synthesizer, which is based on the GARIC (Generalized Approximate Reasoning for Intelligent Control) architecture, is proposed for the problem of biped dynamic balance. We modify the GARIC architecture to enable it to generate the trunk trajectory in both sagittal and frontal plane. The proposed gait synthesizer is trained by reinforcement learning that uses a multi-valued scalar signal to evaluate the degrees of failure or success for the biped locomotion by means of the ZMP (Zero Moment Point). It can form the initial dynamic balancing gait from linguistic rules, which are obtained from human intuitive balancing knowledge and biomechanics studies, and accumulate dynamic balancing knowledge through reinforcement learning, and thus constantly improve its gait during walking. The feasibility of the proposed method is verified through a 5-link biped robot simulation.     

Model and control of the locomotion of a biomimic musculoskeletal biped

This article presents a biomimic musculoskeletal biped which contains 7 segments and 18 muscles. The muscle model and body dynamics are constructed based on physiological theories. A motor control system is designed to mimic natural human locomotion, which contains a central pattern generator, a regulator, a compensator, and an impedance controller. The recurrent neural oscillator models the central pattern generator, and an artificial neural network is used to design the regulator. From the simulation study, we found that this biped can produce a rhythmic and stable walking movement similar to actual human walking.     

Reflex control of bipedal locomotion on a slippery surface

Biped robots are expected to walk on many different and previously unknown terrains including slippery surfaces on which no prior information is available. It is very important that biped robots have an ability to walk on a slippery surface which it meets so suddenly, since any damage to biped robots will be very costly. In order to prevent falling down on a suddenly encountered slippery surface, this paper proposes a reflex control method for biped robots to quickly recover their posture from a foot slip upon its detection. Computer simulations were performed with a 12-d.o.f. biped robot model and a 6-d.o.f. elastic pad model, the latter of which consists of nonlinear dampers, and linear and nonlinear springs. Simulation results show that the proposed method is very effective in preventing biped robots falling down when walking on a slippery surface.     

Balance recovery control for biped robot based on reaction null space method

A biped walking robot should be able to keep balance even in the presence of disturbing forces.This paper presents a step strategy concept of biped walking robot that is stabilized by using reaction null space method.The called "step strategy" can be modeled by means of the reaction null space method that introduced earlier to tackle dynamic interaction problems of free-floating robots,or moving base robots in general.6-DOF biped robot model simulations are used to confirm the validity.     

Real time implementation of CTRNN and BPTT algorithm to learn on-line biped robot balance: Experiments on the standing posture

This paper describes experimental results regarding the real time implementation of continuous time recurrent neural networks (CTRNN) and the dynamic back-propagation through time (BPTT) algorithm for the on-line learning control laws. Experiments are carried out to control the balance of a biped robot prototype in its standing posture. The neural controller is trained to compensate for external perturbations by controlling the torso’s joint motions. Algorithms are embedded in the real time electronic unit of the robot. On-line learning implementations are presented in detail. The results on learning behavior and control performance demonstrate the strength and the efficiency of the proposed approach.     

A study on optimal motion of a biped locomotion machine

In this paper we propose a calculation method for the optimal trajectory of a biped locomotion machine which is based on inverse kinematics and inverse dynamics. First, the trajectory of the waist is expressed by a Fourier series, where the bases are selected appropriately so that the periodic boundary conditions are strictly satisfied. A biped locomotion machine establishes optimal walking by using kicking forces to the ground at the moment of switching legs. In order to include the effecs of the kicking forces, additional terms that indicate the impulsive forces at the moment of switching legs are included in the formulation. Then the angles of each joint are determined by inverse kinematics, and using inverse dynamics, the input torques of each joint are expressed in terms of Fourier coefficients. By defining the performance index as a quadratic form of the input torques, the motion planning problem is formulated as an optimization problem of the trajectory of the waist, whose paramaters are Fourier coefficients of the trajactory of the waist. Using the successive quadratic programming (SQP) method, the optimal trajectory of a biped locomotion machine is obtained. This work was presented, in part, at the Third International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–21, 1998.     

仿人预测控制在双足机器人步行控制中的应用

基于零力矩点(ZMP)的预测控制是目前双足机器人步行控制中最先进的方法,但是预测控制需要比较精确的预测模型,在环境扰动导致模型失配时,预测控制的性能下降较快。为了解决这个问题,利用仿人智能控制对环境误差具有较强抑制的特点改进预测控制。探讨了在步行控制中引入仿人智能控制的必要性和仿人智能控制改进预测控制的可行性,并设计了仿人预测控制器。最后通过仿真实验验证了新的控制器对双足机器人步行控制的有效性。     

Development of a Leg Part of a Humanoid Robot—Development of a Biped Walking Robot Adapting to the Humans' Normal Living Floor

The authors are engaged in studies of biped walking robots from thefollowing two viewpoints. One is a viewpoint as a human science. Theother is a viewpoint towards the development of humanoid robots.In this paper, the authors introduce an anthropomorphic dynamic bipedwalking robot adapting to the humans' living floor. The robot has tworemarkable systems: (1) a special foot system to obtain the positionrelative to the landing surface and the gradient of the surfaceduring its dynamic walking; (2) an adaptive walking control system toadapt to the path surfaces with unknown shapes by utilizing theinformation of the landing surface, obtained by the foot system. Twounits of the foot system WAF-3 were produced, a biped walking robotWL-12RVII that had the foot system and the adaptive walking controlsystem installed inside it was developed, and a walking experimentwith WL-12RVII was performed. As a result, dynamic biped walkingadapting to humans' floors with unknown shapes was realized. Themaximum walking speed was 1.28 s/step with a 0.3 m step length, andthe adaptable deviation range was from -16 to+16 mm/step in the vertical direction, and from-3 to +3° in the tilt angle.     

A SVM controller for the stable walking of biped robots based on small sample sizes

Conventional machine learning methods such as neural network (NN) uses empirical risk minimization (ERM) based on infinite samples, which is disadvantageous to the gait learning control based on small sample sizes for biped robots walking in unstructured, uncertain and dynamic environments. Aiming at the stable walking control problem in the dynamic environments for biped robots, this paper puts forward a method of gait control based on support vector machines (SVM), which provides a solution for the learning control issue based on small sample sizes. The SVM is equipped with a mixed kernel function for the gait learning. Using ankle trajectory and hip trajectory as inputs, and the corresponding trunk trajectory as outputs, the SVM is trained based on small sample sizes to learn the dynamic kinematics relationships between the legs and the trunk of the biped robots. Robustness of the gait control is enhanced, which is propitious to realize the stable biped walking, and the proposed method shows superior performance when compared to SVM with radial basis function (RBF) kernels and polynomial kernels, respectively. Simulation results demonstrate the superiority of the proposed methods.     

Development of a compliance controller to reduce energy consumption for bipedal robots

In this paper a strategy is proposed to combine active trajectory tracking for bipedal robots with exploiting the natural dynamics by simultaneously controlling the torque and stiffness of a compliant actuator. The goal of this research is to preserve the versatility of actively controlled humanoids, while reducing their energy consumption. The biped Lucy, powered by pleated pneumatic artificial muscles, has been built and controlled and is able to walk up to a speed of 0.15 m/s. The pressures inside the muscles are controlled by a joint trajectory tracking controller to track the desired joint trajectories calculated by a trajectory generator. However, the actuators are set to a fixed stiffness value. In this paper a compliance controller is presented to reduce the energy consumption by controlling the stiffness. A mathematical formulation has been developed to find an optimal stiffness setting depending on the desired trajectory and physical properties of the system and the proposed strategy has been validated on a pendulum structure powered by artificial muscles. This strategy has not been implemented on the real robot because the walking speed of the robot is currently too slow to benefit already from compliance control.

Adaptive behavior in turning of an oscillator-driven biped robot

This paper concentrates on a biped robot’s turning behavior that consists of straight and curved walking and the transition between these two patterns. We investigate how a robot achieves adaptive walking during such turning by focusing on rhythm control and propose a locomotion control system that generates robot motions by rhythmic signals from internal oscillators and modulates signal generation based on touch sensor signals. First, we verify that the robot attains limit cycles of straight and curved walking by numerical simulations and hardware experiments. Second, we examine the transition between these walking patterns based on the basin of attraction of the limit cycles in numerical simulations. Finally, we verify whether the robot actually accomplishes transition and turning by hardware experiments. This paper clarifies that the robot establishes such turning motions by adequate modulation of walking rhythm and phase through interactions between the dynamics of its mechanical system, oscillators, and environment.

Decreased vibration control for centrifuges: A new adaptive hybrid control technique

This paper presents a new control approach which can restrain the vibration of centrifuges. In the new scheme, changed support stiffness and self-tuning feedforward PID control of the decreased vibration force are effectively combined. Some advanced techniques, (such as adaptive modification for unstable vibration regions, two-level computer control, curve-tracking control, are used to make the centrifuge system run in a minimum-vibration state. A horizontal centrifugal experiment is used to test the new control method. Experimental results show the effectiveness of the proposed scheme.