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.

Learning Robust Locomotion for Bipedal Robot via Embedded Mechanics Properties

Reinforcement learning(RL)provides much potential for locomotion of legged robot.Due to the gap between simulation and the real world,achieving sim-to-real for legged robots is challenging.However,the support polygon of legged robots can help to overcome some of these challenges.Quadruped robot has a considerable support polygon,followed by bipedal robot with actuated feet,and point-footed bipedal robot has the smallest support polygon.Therefore,despite the existing sim-to-real gap,most of the recent RL approaches are deployed to the real quadruped robots that are inherently more stable,while the RL-based locomotion of bipedal robot is challenged by zero-shot sim-to-real task.Especially for the point-footed one that gets better dynamic performance,the inevitable tumble brings extra barriers to sim-to-real task.Actually,the crux of this type of problem is the difference of mechanics properties between the physical robot and the simulated one,making it difficult to play the learned skills well on the physical bipedal robot.In this paper,we introduce the embedded mechanics properties(EMP)based on the optimization with Gaussian processes to RL training,making it possible to perform sim-to-real transfer on the BRS1-P robot used in this work,hence the trained policy can be deployed on the BRS1-P without any struggle.We validate the performance of the learning-based BRS1-P on the condition of disturbances and terrains not ever learned,demonstrating the bipedal locomotion and resistant performance.

Push recovery for the standing under-actuated bipedal robot using the hip strategy

This paper presents a control algorithm for push recovery, which particularly focuses on the hip strategy when an external disturbance is applied on the body of a standing under-actuated biped. By analyzing a simplified dynamic model of a bipedal robot in the stance phase, it is found that horizontal stability can be maintained with a suitably controlled torque applied at the hip. However, errors in the angle or angular velocity of body posture may appear, due to the dynamic coupling of the transla- tional and rotational motions. To solve this problem, different hip strategies are discussed for two cases when （1） external dis- turbance is applied on the center of mass （CoM） and （2） external torque is acting around the CoM, and a universal hip strategy is derived for most disturbances. Moreover, three torque primitives for the hip, depending on the type of disturbance, are designed to achieve translational and rotational balance recovery simultaneously. Compared with closed-loop control, the advantage of the open-loop methods of torque primitives lies in rapid response and reasonable performance. Finally, simulation studies of the push recovery of a bipedal robot are presented to demonstrate the effectiveness of the proposed methods.

Squat motion of a bipedal robot using real-time kinematic prediction and whole-body control

Squatting is a basic movement of bipedal robots,which is essential in robotic actions like jumping or picking up objects.Due to the intrinsic complex dynamics of bipedal robots,perfect squatting motion requires high-performance motion planning and control algorithms.The standard academic solution combines model predictive control(MPC)with whole-body control(WBC),which is usually computationally expensive and difficult to implement on practical robots with limited computing resources.The real-time kinematic prediction(RKP)method is proposed,which considers upcoming reference motion trajectories and combines it with quadratic programming(QP)-based WBC.Since the WBC handles the full robot dynamics and various constraints,the RKP only needs to adopt the linear kinematics in the robot's task space and to softly constrain the desired accelerations.Then,the computational cost of derived closed-form RKP is greatly reduced.The RKP method is verified in simulation on a heavy-loaded bipedal robot.The robot makes rapid and large-amplitude squatting motions,which require close-to-limit torque outputs.Compared with the conventional QP-based WBC method,the proposed method exhibits high adaptability to rough planning,which implies much less user interference in the robot's motion planning.Furthermore,like the MPC,the proposed method can prepare for upcoming motions in advance but requires much less computation time.

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.

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.

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.

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.

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.

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.

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.

Study on Gait Planning of Dynamic Walking of Biped Robots Based on Optimization Theory

In this paper, two important problems in the gait planning of dynamic walking of biped robot, i.e., finding inverse kinematic solution and constructing joint trajectories, are studied in detail by adopting complex optimization theory. The optimization algorithm for finding the inverse kinematic solution is developed, the construction method of joint trajectories is given, and the gait planning method of dynamic walking of biped robots is proposed.

LIE SYMMETRIES AND CONSERVED QUANTITY OF A BIPED ROBOT

For a better understanding of the dynamic principles governing biped locomotion, the Lie symmetries and conservation laws of a biped robot are studied. In Lie theory, Lie sym- metries and conservation laws can be derived from the form invariance of di?erential equations undergoing in?nitesimal transformation. By introducing in?nitesimal transformations including time and spatial coordinates, the determining equations of a biped robot are established. Then the necessary and su?cient conditions for a biped robot to have conserved quantities are obtained. For the lateral-plane dynamical model of a biped robot, a Lie conserved quantity is found.

Dynamic Analysis of the Biped Ice-skater Robot of Passive Wheel Type

A new passive wheel type of biped ice-skater robot (BISR) subjected to nonholonomic constraints was presented on the basis of ice-skating principle. Its motion principle and construction were discussed. After the model was simplified and the coordinate systems were established, the motion differential equations of the robot were obtained with the generalized Lagrange-Maggi equation when the nonholonomic constraints existed. Actual examples were given and the result was simulated on computer.

Incorporation of Perception-based Information in Robot Learning Using Fuzzy Reinforcement Learning Agents

Robot learning in unstructured environments has been proved to be an extremely challenging problem, mainly because of many uncertainties always present in the real world. Human beings, on the other hand, seem to cope very well with uncertain and unpredictable environments, often relying on perception-based information. Furthermore, humans beings can also utilize perceptions to guide their learning on those parts of the perception-action space that are actually relevant to the task. Therefore, we conduct a research aimed at improving robot learning through the incorporation of both perception-based and measurement-based information. For this reason, a fuzzy reinforcement learning (FRL) agent is proposed in this paper. Based on a neural-fuzzy architecture, different kinds of information can be incorporated into the FRL agent to initialise its action network, critic network and evaluation feedback module so as to accelerate its learning. By making use of the global optimisation capability of GAs (genetic algorithms), a GA-based FRL (GAFRL) agent is presented to solve the local minima problem in traditional actor-critic reinforcement learning. On the other hand, with the prediction capability of the critic network, GAs can perform a more effective global search. Different GAFRL agents are constructed and verified by using the simulation model of a physical biped robot. The simulation analysis shows that the biped learning rate for dynamic balance can be improved by incorporating perception-based information on biped balancing and walking evaluation. The biped robot can find its application in ocean exploration, detection or sea rescue activity, as well as military maritime activity.

Development of Wheel-Legged Biped Robots:A Review

The wheel-legged biped robot is a typical ground-based mobile robot that can combine the high velocity and high efficiency pertaining to wheeled motion and the strong,obstacle-crossing performance associated with legged motion.These robots have gradually exhibited satisfactory application potential in various harsh scenarios such as rubble rescue,military operations,and wilderness exploration.Wheel-legged biped robots are divided into four categories according to the open–close chain structure forms and operation task modes,and the latest technology research status is summarized in this paper.The hardware control system,control method,and application are analyzed,and the dynamic balance control for the two-wheel,biomimetic jumping control for the legs and whole-body control for integrating the wheels and legs are analyzed.In summary,it is observed that the current research exhibits problems,such as the insufficient application of novel materials and a rigid–flexible coupling design;the limited application of the advanced,intelligent control methods;the inadequate understanding of the bionic jumping mechanisms in robot legs;and the insufficient coordination ability of the multi-modal motion,which do not exhibit practical application for the wheel-legged biped robots.Finally,this study discusses the key research directions and development trends for the wheel-legged biped robots.

Development of Minimalist Bipedal Walking Robot with Flexible Ankle and Split-mass Balancing Systems

This paper presents a novel design of minimalist bipedal walking robot with flexible ankle and split-mass balancing systems.The proposed approach implements a novel strategy to achieve stable bipedal walk by decoupling the walking motion control from the sideway balancing control.This strategy allows the walking controller to execute the walking task independently while the sideway balancing controller continuously maintains the balance of the robot.The hip-mass carry approach and selected stages of walk implemented in the control strategy can minimize the efect of major hip mass of the robot on the stability of its walk.In addition,the developed smooth joint trajectory planning eliminates the impacts of feet during the landing.In this paper,the new design of mechanism for locomotion systems and balancing systems are introduced.An additional degree of freedom introduced at the ankle joint increases the sensitivity of the system and response time to the sideway disturbances.The efectiveness of the proposed strategy is experimentally tested on a bipedal robot prototype.The experimental results provide evidence that the proposed strategy is feasible and advantageous.

Online gait programming of humanoid walking via NMPC

In order to satisfy the requirement of realtime gait programming of humanoid walking with foot rotation,a kind of modified Nonlinear Model Predictive Control (NMPC) scheme was proposed. Based on setting suitable kinetic and kinematic virtual constraints of Single Support Phase (SSP) and three subphases of Double Support Phase (DSP) ,complex realtime gait programming problem was simplified to four online NMPC dynamic optimization problems. A numerical approach was proposed to transform the dynamical optimization problem to the finite dimensional static optimization problem which can be solved by Sequential Quadratic Programming (SQP) . It can be concluded from simulation that using this method on BIP model can realize online gait programming of dynamic walking with foot rotation and the biped stability can be satisfied such that there is no sliding during walking.

CPG Control for Biped Hopping Robot in Unpredictable Environment

A CPG control mechanism is proposed for hopping motion control of biped robot in unpredictable environment. Based on analysis of robot motion and biological observation of animal＇s control mechanism, the motion control task is divided into two simple parts： motion sequence control and output force control. Inspired by a two-level CPG model, a two-level CPG control mechanism is constructed to coordinate the drivers of robot joint, while various feedback information are introduced into the control mechanism. Interneurons within the control mechanism are modeled to generate motion rhythm and pattern promptly for motion sequence control; motoneurons are modeled to control output forces of joint drivers in real time according to feedbacks. The control system can perceive changes caused by unknown perturbations and environment changes according to feedback information, and adapt to unpredictable environment by adjusting outputs of neurons. The control mechanism is applied to a biped hopping robot in unpredictable environment on simulation platform, and stable adaptive motions are obtained.

Adaptive Walking Control of Biped Robots Using Online Trajectory Genera- tion Method Based on Neural Oscillators

This work concerns biped adaptive walking control on irregular terrains with online trajectory generation. A new trajectory generation method is proposed based on two neural networks. One oscillatory network is designed to generate foot trajectory, and another set of neural oscillators can generate the trajectory of Center of Mass （CoM） online. Using a motion engine, the characteristics of the workspace are mapped to the joint space. The entraining property of the neural oscillators is exploited for adaptive walking in the absence of a priori knowledge of walking conditions. Sensory feedback is applied to modify the gen- erated trajectories online to improve the walking quality. Furthermore, a staged evolutionary algorithm is developed to tune system parameters to improve walking performance. The developed control strategy is tested using a humanoid robot on ir- regular terrains. The experiments verify the success of the presented strategy. The biped robot can walk on irregular terrains with varying slopes, unknown bumps and stairs through autonomous adjustment of its walking patterns.