Kinematic analysis of flexible bipedal robotic systems

In spite of its intrinsic complexities,the passive gait of bipedal robots on a sloping ramp is a subject of interest for numerous researchers.What distinguishes the present research from similar works is the consideration of flexibility in the constituent links of this type of robotic systems.This is not a far-fetched assumption because in the transient(impact)phase,due to the impulsive forces which are applied to the system,the likelihood of exciting the vibration modes increases considerably.Moreover,the human leg bones that are involved in walking are supported by viscoelastic muscles and ligaments.Therefore,for achieving more exact results,it is essential to model the robot links with viscoelastic properties.To this end,the Gibbs-Appell formulation and Newton's kinematic impact law are used to derive the most general form of the system's dynamic equations in the swing and transient phases of motion.The most important issue in the passive walking motion of bipedal robots is the determination of the initial robot configuration with which the system could accomplish a periodic and stable gait solely under the effect of gravitational force.The extremely unstable nature of the system studied in this paper and the vibrations caused by the impulsive forces induced by the impact of robot feet with the inclined surface are some of the very serious challenges encountered for achieving the above-mentioned goal.To overcome such challenges,an innovative method that uses a combination of the linearized equations of motion in the swing phase and the algebraic motion equations in the transition phase is presented in this paper to obtain an eigenvalue problem.By solving this problem,the suitable initial conditions that are necessary for the passive gait of this bipedal robot on a sloping surface are determined.The effects of the characteristic parameters of elastic links including the modulus of elasticity and the Kelvin-Voigt coefficient on the walking stability of this type of robotic systems are also studied.The findings of this parametric study reveal that the increase in the Kelvin-Voigt coefficient enhances the stability of the robotic system,while the increase in the modulus of elasticity has an opposite effect.

Balance Control of a Biped Robot on a Rotating Platform Based on Efficient Reinforcement Learning

In this work,we combined the model based reinforcement learning(MBRL)and model free reinforcement learning(MFRL)to stabilize a biped robot(NAO robot)on a rotating platform,where the angular velocity of the platform is unknown for the proposed learning algorithm and treated as the external disturbance.Nonparametric Gaussian processes normally require a large number of training data points to deal with the discontinuity of the estimated model.Although some improved method such as probabilistic inference for learning control(PILCO)does not require an explicit global model as the actions are obtained by directly searching the policy space,the overfitting and lack of model complexity may still result in a large deviation between the prediction and the real system.Besides,none of these approaches consider the data error and measurement noise during the training process and test process,respectively.We propose a hierarchical Gaussian processes(GP)models,containing two layers of independent GPs,where the physically continuous probability transition model of the robot is obtained.Due to the physically continuous estimation,the algorithm overcomes the overfitting problem with a guaranteed model complexity,and the number of training data is also reduced.The policy for any given initial state is generated automatically by minimizing the expected cost according to the predefined cost function and the obtained probability distribution of the state.Furthermore,a novel Q(λ)based MFRL method scheme is employed to improve the policy.Simulation results show that the proposed RL algorithm is able to balance NAO robot on a rotating platform,and it is capable of adapting to the platform with varying angular velocity.

Biped Walking Robot Based on a 2-UPU+2-UU Parallel Mechanism

Existing biped robots mainly fall into two categories： robots with left and right feet and robots with upper and lower feet. The load carrying capability of a biped robot is quite limited since the two feet of a walking robot supports the robot alternatively during walking. To improve the load carrying capability, a novel biped walking robot is proposed based on a 2-UPU＋2-UU parallel mechanism. The biped walking robot is composed of two identical platforms（feet） and four limbs, including two UPU（universal-prismatic-universal serial chain） limbs and two UU limbs. To enhance its terrain adaptability like articulated vehicles, the two feet of the biped walking robot are designed as two vehicles in detail. The conditions that the geometric parameters of the feet must satisfy are discussed. The degrees-of-freedom of the mechanism is analyzed by using screw theory. Gait analysis, kinematic analysis and stability analysis of the mechanism are carried out to verify the structural design parameters. The simulation results validate the feasibility of walking on rugged terrain. Experiments with a physical prototype show that the novel biped walking robot can walk stably on smooth terrain. Due to its unique feet design and high stiffness, the biped walking robot may adapt to rugged terrain and is suitable for load-carrying.

Biped Robot with Triangle Configuration

A new biped robot with a triangle configuration is presented and it is a planar closed chain mechanism. The scalability of three sides of the triangle is realized by three actuated prismatic joints. The three vertexes of the triangle are centers of three passive revolute joints coincidently. The biped mechanism for straight walking is proposed and its walking principle and mobility are explained. The static stability and the height and span of one step are analyzed. Kinematic analysis is performed to plan the gaits of walking on an even floor and going upstairs. A prototype is developed and experiments are carried out to validate the straight walking gait. Two additional revolute joints are added to form a modified biped robot which can follow the instruction of turning around. The turning ability is verified by experiments. As a new member of biped robots, its triangle configuration is used to impart geometry knowledge. Because of its high stiffness, some potential applications are on the way.

Planning and Control of COP-Switch-Based Planar Biped Walking

Efficient walking is one of the main goals of researches on biped robots. A feasible way is to translate the understanding from human walking into robot walking, for example, an artificial control approach on a human like walking structure. In this paper, a walking pattern based on Center of Pressure （COP） switched and modeled after human walking is introduced firstly. Then, a parameterization method for the proposed walking gait is presented. In view of the complication, a multi-space planning method which divides the whole planning task into three sub-spaces, including simplified model space, work space and joint space, is proposed. Furthermore, a finite-state-based control method is also developed to implement the proposed walking pattern. The state switches of this method are driven by sensor events. For convincing verification, a 2D simulation system with a 9-1ink planar biped robot is developed. The simulation results exhibit an efficient walking gait.

Dynamical analysis and performance evaluation of a biped robot under multi-source random disturbances

During bipedal walking,it is critical to detect and adjust the robot postures by feedback control to maintain its normal state amidst multi-source random disturbances arising from some unavoidable uncertain factors.The radical basis function（RBF）neural network model of a five-link biped robot is established,and two certain disturbances and a randomly uncertain disturbance are then mixed with the optimal torques in the network model to study the performance of the biped robot by several evaluation indices and a specific Poincar′e map.In contrast with the simulations,the response varies as desired under optimal inputting while the output is fluctuating in the situation of disturbance driving.Simulation results from noise inputting also show that the dynamics of the robot is less sensitive to the disturbance of knee joint input of the swing leg than those of the other three joints,the response errors of the biped will be increasing with higher disturbance levels,and especially there are larger output fluctuations in the knee and hip joints of the swing leg.

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.

Impactless biped walking on a slope

Walking without impacts has been considered in dynamics as a motion/force control problem. In order to avoid impacts, an approach for both the specified motion of the biped and its ground reaction forces was presented yielding a combined motion and force control problem. As an application, a walker on a horizontal plane has been considered. In this paper, it is shown how the control of the ground reaction forces and the energy consumption depend on the gradient of a slope. The biped dynamics and the constraints within the biped system and on the ground are discussed. A motion control synthesis is developed using the inverse dynamics principle proven to be most efficient for human walking research, too. The impactless walking with controlled legs is illustrated by a seven-link biped. The ＂flying＂ biped has nine degrees of freedom, with six control inputs. During locomotion, the standing leg has three scleronomic constraints, and the trunk has three rheonomic constraints. However, there are three rheonomic constraints for the prescribed leg motion or three scleronomic constraints for reaction forces of the trailing leg, respectively. The nominal control action for impactless walking can be precomputed and stored. The model proposed allows the investigation of several problems： uphill and downhill walking, optimization of step length,stiction of the feet on the slope and many more. All these findings are also of interest in biomechanics. C 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1301302]

STUDIES ON MECHANICS PROBLEM OF DYNAMIC WALKING OF ANTHROPOMORPHIC BIPED ROBOTS

This paper deals with the mechanics problem of dynamic walking of anthropomorphic biped robots. Through analysing the mechanics system of this kind of robots in detail, the motion constraint equations are established, three mechanics laws describing the r

Input torque sensitivity to uncertain parameters in biped robot

Input torque is the main power to maintain bipedal walking of robot, and can be calculated from trajectory planning and dynamic modeling on biped robot. During bipedal walking, the input torque is usually required to be adjusted due to some uncertain parameters arising from objective or subjective factors in the dynamical model to maintain the pre-planned stable trajectory. Here, a planar 5-link biped robot is used as an illustrating example to investigate the effects of uncertain parameters on the input torques. Kine-matic equations of the biped robot are firstly established by the third-order spline curves based on the trajectory planning method, and the dynamic modeling is accomplished by taking both the certain and uncertain parameters into account. Next, several evaluation indices on input torques are intro-duced to perform sensitivity analysis of the input torque with respect to the uncertain parameters. Finally, based on the Monte Carlo simulation, the values of evaluation indices on input torques are presented, from which all the robot param-eters are classified into three categories, i.e., strongly sensi-tive, sensitive and almost insensitive parameters.

OPTIMIZATION OF THE BIPED ROBOT GAIT USING GENETIC ALGORITHM

Based on the 7-link dynamic model in the sagittal plane and the 5-link dynamic model in the lateral plane, the parametric gait of the biped robot is designed using walking velocity, step length and height of the hip. According to the condition of the stability, body swings forward and backward to dynamically balance in sagittal plane and the whole biped swings left and right to dynamically balance in lateral plane. And the genetic algorithm is applied to obtain the optimal parameters on condition of keeping dynamic stability and the minimizing of the value of the dynamic balance.

Influence of Slope Angle on the Walking of Passive Dynamic Biped Robot

In this paper, we modeled a simple planer passive dynamic biped robot without knee with point feet. This model has a stable, efficient and natural periodic gait which depends on the values of parameters like slope angle of inclined ramp, mass ratio and length ratio. The described model actually is an impulse differential equation. Its corresponding poincare map is discrete case. With the analysis of the bifurcation properties of poincare map, we can effectively understand some feature of impulse model. The ideas and methods to cope with this impulse model are common. But, the process of analysis is rigorous. Numerical simulations are reliable.

ZMP-based Gait Optimization of the Biped Robot

The gait of the biped robot is described using six parameters such as stature,velocity,length of the step,etc.The algorithm of the Newton-Euler is actualized by object-oriented idea,and then the zero moment point (ZMP) of the dynamically walking biped is calculated.Finally,the gait of biped is optimized using gene algorithm,and the optimized result prove the correctness of the algorithm.

Modeling and analysis of passive dynamic bipedal walking with segmented feet and compliant joints

Passive dynamic walking has been developed as a possible explanation for the efficiency of the human gait. This paper presents a passive dynamic walking model with segmented feet, which makes the bipedal walking gait more close to natural human-like gait. The proposed model extends the simplest walking model with the addition of fiat feet and torsional spring based compliance on ankle joints and toe joints, to achieve stable walking on a slope driven by gravity. The push-off phase includes foot rotations around the toe joint and around the toe tip, which shows a great resemblance to human normal walking. This paper investigates the effects of the segmented foot structure on bipedal walking in simulations. The model achieves satisfactory walking results on even or uneven slopes.

Walking Stability Control Method for Biped Robot on Uneven Ground Based on Deep Q-Network

A gait control method for a biped robot based on the deep Q-network (DQN) algorithm is proposed to enhance the stability of walking on uneven ground. This control strategy is an intelligent learning method of posture adjustment. A robot is taken as an agent and trained to walk steadily on an uneven surface with obstacles, using a simple reward function based on forward progress. The reward-punishment (RP) mechanism of the DQN algorithm is established after obtaining the offline gait which was generated in advance foot trajectory planning. Instead of implementing a complex dynamic model, the proposed method enables the biped robot to learn to adjust its posture on the uneven ground and ensures walking stability. The performance and effectiveness of the proposed algorithm was validated in the V-REP simulation environment. The results demonstrate that the biped robot's lateral tile angle is less than 3° after implementing the proposed method and the walking stability is obviously improved.

Robust State Feedback H_∞Control for Dynamic Biped Robot Based on T-S Fuzzy Model

T-S fuzzy model was applied to describe nonlinear system and global fuzzy model was expressed by the form of uncertain system.Based on robust state feedback H_∞control strategy,designed a global asymptotic steady fuzzy model.This control system can use the experimental input-output data pairs for the biped robot learning and walking with dynamic balance.It is proved by simulation result that robust state feedback H_∞control method based on T-S fuzzy model can effectively restrain the effect of model uncertainties and external disturbance acting on biped robot.From these works,we showed the satisfactory performance of joint tracking without any chattering.

Study and Development of the Biped Ice Skating Robot with Passive Wheels

A new passive wheel type of biped ice-skating robot(BISR)which was able to imitate human skating motion was developed. Firstly, the characteristics of two types of human skating gait were introduced; secondly, after simplifying the kinematical model, the BISR's motion principle was presented; then the construction and control system of BISR were proposed; at last, the skating experiment of the BISR in a symmetric gait mode was conducted and some conclusions were drawn.

A NEW METHOD OF MECHANISM SYNTHESIS FOR BIPED ROBOTS

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A novel compound biped locomotion algorithm for humanoid robots to realize biped walking

In this paper, a compound biped locomotion algorithm for a humanoid robot under development is presented. This paper is organized in two main parts. In the first part, it mainly focuses on the structural design for the humanoid. In the second part, the compound biped locomotion algorithm is presented based on the reference motion and reference Zero Moment Point （ZMP）. This novel algorithm includes calculation of the upper body motion and trajectory of the Center of Gravity （COG） of the robot. First, disturbances from the environment are eliminated by the compensational movement of the upper body; then based on the error between a reference ZMP and the real ZMP as well as the relation between ZMP and CoG, the CoG error is calculated, thus leading to the CoG trajectory. Then, the motion of the robot converges to its reference motion, generating stable biped walking. Because the calculation of upper body motion and trajectory of CoG both depend on the reference motion, they can work in parallel, thus providing double insurances against the robot＇s collapse. Finally, the algorithm is validated by different kinds of simulation experiments.

Biped 4R2C Six-bar Mechanism with Inner and Outer Feet

Most current biped robots are equipped with two feet arranged in the right and left which inspired by the human body system. Different from the existing configurations, a novel biped robot with inner and outer feet based on a spatial six-bar 4R2C（R and C denote revolute and cylindric joints, respectively） mechanism is proposed. It can move along a line or a curve by three walking modes that are dwell adjustment mode, limit position adjustment mode and any position adjustment mode. Kinematic, gait planning and stability analyses are performed respectively, and a prototype is developed. Lastly, a potential application is considered and two manipulating modes（sphere and cylinder manipulating modes） are carried out. This interesting mechanism feathering its single dosed-chain structure and unique work performance is expected to motivate the configuration creation of biped robots.