Biped Robot Model Research Articles

A simple bipedal robot model demonstrating speed-dependent gait transition

Abstract This paper introduces a novel bipedal robot model designed for adaptive transition between walking and running gaits solely through changes in locomotion speed. The bipedal robot model comprises two sub-components: a mechanical model for the legs that accommodates both walking and running and a continuous state model that does not explicitly switch states. The mechanical model employs a structure combining a linear cylinder with springs, dampers, and stoppers, designed to have mechanistic properties of both the inverted pendulum model used for walking and the spring-loaded inverted pendulum model used for running. The state model utilizes a virtual leg representation to abstractly describe the actual support leg, capable of commonly representing both a double support leg in walking and a single support leg in running. These models enable a simple gait controller to determine the kick force and the foot touchdown point based solely on the parameter of the target speed, thus allowing a robot to walk and run stably. Hence, simulation validation demonstrates the adaptive robot transition to an energy-efficient gait depending on locomotion speed without explicit gait-type instructions and maintaining stable locomotion across a wide range of speeds.

Piezoelectric energy harvesting from walking motion of a passive biped robot model with flexible legs

Passive dynamic walking biped robots utilize the inherent dynamics of their structure to achieve walking motion without continuous actuation, enhancing energy efficiency and stability. Replacing conventional rigid legs with flexible elastic beams in the simplest passive walker will be associated with undesirable vibrations. Despite the positive effect of the damper in reducing vibrations, the current research has used the piezoelectric energy harvesting with the aim of reducing the wasted energy of the gait cycle and improving its stability range. For this purpose, the electromechanical Lagrange equations are determined by applying Hamilton's principle and the assumed mode method and then, the new definition of the step function is obtained through numerical methods, solving a boundary value problem to establish proper initial conditions for stable walking. Numerical simulations indicate that the piezoelectric energy harvester can create a stable period-one gait cycle by optimizing the length of the piezo layers attached to the undamped elastic legs despite the presence of small vibrations. Additional results are presented in bifurcation diagrams, investigating the effect of important physical and structural parameters such as slope angle, length and thickness of the piezo layer.

Dynamic modeling of wheeled biped robot and controller design for reducing chassis tilt angle

AbstractThe wheeled-legged robot combines the advantages of wheeled and legged robots, making it easier to assist people in completing repetitive and time-consuming tasks in their daily lives. This paper presents a study on the kinematic and dynamic modeling, as well as the controller design, of a wheeled biped robot with a parallel five-bar linkage mechanism as its leg module. During the motion of the robot, the robot relies on the tilt angle of the inverted pendulum, and this angle often results in the tilting of the chassis of the robot, presenting challenges for the installation of upper-body payloads and sensor systems. The controller proposed in this paper, which is developed by decoupling the primary motions of the robot and designing a multi-objective, multilevel controller, addresses this issue. This controller employs the pendulum pitch angle of the equivalent inverted pendulum model as the control variable and compensates for the chassis tilt angle (CTA). This control method can effectively reduce the CTA of such robots and eliminate the need for additional counterweights. It also provides a more spacious structural design for accommodating upper-body devices. The effectiveness of this control framework is verified through variable height control, walking on flat ground, and carrying loads over rough terrain and slopes.

Bounding gait control of a parallel quadruped robot

PurposeThe computing power of the legged robot is not enough to perform high-frequency updates for the full-body model predictive control (MPC) of the robot, which is a common problem encountered in the gait research of the legged robot. The purpose of this paper is to propose a high-frequency MPC control method for the bounding gait of a parallel quadruped robot.Design/methodology/approachAccording to the bounding gait characteristics of the robot, the quadruped robot model is simplified to an equivalent plane bipedal model. Under the biped robot model, the forces between the robot’s feet and the ground are calculated by MPC. Then, the authors apply a proportional differential controller to distribute these forces to the four feet of the quadruped robot. The robot video can be seen at www.bilibili.com/video/BV1je4y1S7Rn.FindingsTo verify the feasibility of the controller, a prototype was made, and the controller was deployed on the actual prototype and then fully analyzed through experiments. Experiments show that the update frequency of MPC could be stabilized at 500 Hz while the robot was running in the bounding gait stably and efficiently.Originality/valueThis paper proposes a high-frequency MPC controller under the simplified model, which has a higher working efficiency and more stable control performance.

Occurrence of Complex Behaviors in the Uncontrolled Passive Compass Biped Model

It is widely known that an appropriately built unpowered bipedal robot can walk down an inclined surface with a passive steady gait. The features of such gait are determined by the robot's geometry and inertial properties, as well as the slope angle. The energy needed to keep the biped moving steadily comes from the gravitational potential energy as it descends the inclined surface. The study of such passive natural motions could lead to ideas for managing active walking devices and a better understanding of the human locomotion. The major goal of this study is to further investigate order, chaos and bifurcations and then to demonstrate the complexity of the passive bipedal walk of the compass-gait biped robot by examining different bifurcation diagrams and also by studying the variation of the eigenvalues of the Poincaré map's Jacobian matrix and the variation of the Lyapunov exponents. We reveal also the exhibition of some additional results by changing the inertial and geometrical parameters of the bipedal robot model.

A hybrid chaotic controller integrating hip stiffness modulation and reinforcement learning-based torque control to stabilize passive dynamic walking

Implementation of bipedal stable walking has attracted a lot of interest. Passive dynamic walking (PDW) is one promising manner to generate natural bipedal walking with high energy efficiency. However, how to improve stability and versatility of PDW-based robot against disturbance and time varying environments is still a big challenge in robotics. Chaos and bifurcations are intrinsic features of biped dynamic walking, which are important reasons for the failure of PDW. Thus a hybrid chaotic controller to stabilize chaos and bifurcations of PDW was proposed in this paper. At first, the dynamics model of compliant biped robot was set up, and routine to bipedal chaotic motions was found through parameter study. Then one hybrid chaotic controller integrating hip stiffness modulation and hip impulse torque control was developed, where hip impulse torque control based on reinforcement learning was trained to get state variables close to fixed point of PDW, and then hip stiffness modulation was conducted based on Ott-Grebogi-Yorke method to stabilize unstable motions of fixed point. Simulation results showed that period-1 stable walking could be gained for biped robots from chaotic motions, against original value disturbance, force disturbance and in time varying environments. The proposed hybrid chaotic controller could be used to stabilize bipedal chaotic motions and make the passivity-based robot become robust and versatile to disturbed and time changing environments.

Modeling and Control of a Wheeled Biped Robot.

It is difficult to realize the stable control of a wheeled biped robot (WBR), as it is an underactuated nonlinear system. To improve the balance and dynamic locomotion capabilities of a WBR, a decoupled control framework is proposed. First, the WBR is decoupled into a variable-length wheeled inverted pendulum and a five-link multi-rigid body system. Then, for the above two simplified models, a time-varying linear quadratic regulator and a model predictive controller are designed, respectively. In addition, in order to improve the accuracy of the feedback information of the robot, the Kalman filter is used to optimally estimate the system state. The control framework can enable the WBR to realize changing height, resisting external disturbances, velocity tracking and jumping. The results obtained by simulations and physical experiments verify the effectiveness of the framework.

Leg Configuration Analysis and Prototype Design of Biped Robot Based on Spring Mass Model

The leg structure with high dynamic stability can make the bionic biped robot have the inherent conditions to perform elastic and highly dynamic motion. Compared with the quadruped robot, the leg structure of the biped robot is more complex and has more degrees of freedom. This also complicates kinematic and dynamic modeling. In this paper, the kinematics model of a bionic biped robot is established. The leg configuration of the robot is a series parallel hybrid mechanism with five active joints and six passive joints. The mechanism is a spring mass model that interacts organically with the environment and mimics the characteristics of human walking well. By analyzing the topological configuration of leg mechanism, we use the screw theory to establish the forward and inverse kinematics models. Then, we build the prototype, and use a step gait to test the model and prototype. The research of this paper has obvious application significance for the design and iteration of biped robot prototype.

Pedestrian motion centroid model based on robot dynamics

In recent years, with the rapid development of computer vision technology, image-based human body research has become an important task, such as pedestrian target detection, trajectory tracking, posture estimation and behaviour recognition. The centre of mass is one of the important characteristics that can reflect the phenomenon of pedestrian movement. This paper first introduces the biped robot model in robotics, starting from forward and inverse kinematics, to find the mapping relationship between the position of each joint and the pose of the end effector. Then, corresponding to the skeleton model of the human joint points, the characteristics of the bone posture and joint angle are determined. The moment of inertia factor is introduced, and the motion superposition of different joint points is considered to establish a pedestrian motion centroid model. By calculating the equivalent dynamic centroid, the pedestrian kinematics law can be explored and the pedestrian movement mechanism can be more deeply recognized.

Control and Simulation of a 6-DOF Biped Robot based on Twin Delayed Deep Deterministic Policy Gradient Algorithm

Objectives: To study an algorithm to control a bipedal robot to walk so that it has a gait close to that of a human. It is known that the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm is a highly efficient algorithm with a few changes compared to the popular algorithm — the commonly used Deep Deterministic Policy Gradient (DDPG) in the continuous action space problem in Reinforcement Learning. Methods: Different from the usual sparse reward function model used, in this study, a reward model combined with a sparse reward function and dense reward function will be proposed. The application of the TD3 algorithm together with the proposed reward function model to control a bipedal robot model with 6 degrees of freedom will be presented. The training process is simulated in Gazebo/Robot Operating System (ROS) environment. Finding: The results show that, when choosing a reward model combined with a sparse reward function and a dense reward function suitable for the robot model, will help it learn faster and achieve better results. The biped robot can walk straight with an almost human-like gait. In the paper, the results from the TD3 algorithm combined with the proposed reward model are also compared with the results from other algorithms. Novelty: Applying the TD3 algorithm combined with the proposed reward model for the 6-DOF biped robot and simulating the robot’s gait in Gazebo/ROS environment, ROS is a middleware that can be used to control a robot in a real environment in the future. Keywords: TD3; biped robot; reinforcement learning; ROS; Gazebo

Simulation of Disturbance Recovery Based on MPC and Whole-Body Dynamics Control of Biped Walking.

Biped robots are similar to human beings and have broad application prospects in the fields of family service, disaster rescue and military affairs. However, simplified models and fixed center of mass (COM) used in previous research ignore the large-scale stability control ability implied by whole-body motion. The present paper proposed a two-level controller based on a simplified model and whole-body dynamics. In high level, a model predictive control (MPC) controller is implemented to improve zero moment point (ZMP) control performance. In low level, a quadratic programming optimization method is adopted to realize trajectory tracking and stabilization with friction and joint constraints. The simulation shows that a 12-degree-of-freedom force-controlled biped robot model, adopting the method proposed in this paper, can recover from a 40 Nm disturbance when walking at 1.44 km/h without adjusting the foot placement, and can walk on an unknown 4 cm high stairs and a rotating slope with a maximum inclination of 10°. The method is also adopted to realize fast walking up to 6 km/h.

Bionics Design of Artificial Leg and Experimental Modeling Research of Pneumatic Artificial Muscles

In the research and development of intelligent prosthesis, some of performance test experiments are required. In order to provide an ideal experimental platform for the performance test of intelligent prosthesis, a heterogeneous biped walking robot model is proposed. Artificial leg is an important part of heterogeneous biped walking robot, and its main function is to simulate the disabled a healthy normal gait, which provides intelligent bionic legs gait to follow the target trajectory. The pneumatic artificial muscles (PAM) have good application in the artificial leg. The bionic design of artificial leg mainly includes the structure of hip joint, knee joint, and ankle joint, adopting the four-bar mechanism as the mechanical structure of the knee joint, and PAM are used as the driving source of the knee joint. Secondly, the PAM performance test platform is built to establish the relationship among output force, shrinkage rate, and input pressure under the measured isobaric conditions, and the mathematical model of PAM is established. Finally, the virtual prototype technology is used to build a joint simulation platform, and PID control algorithm is used for verification simulation. The results show that the artificial leg can follow the target trajectory.

Tracking control using optimal discrete-time [formula omitted] for mechanical systems: Applied to Robotics

In this work, the H∞ control for mechanical systems and its application in Robotics is discussed. The controller is designed in discrete time and it is synthesized for mechanical systems that are modeled by means of the Euler–Lagrange formulation. Making use of the discrete Hamilton–Jacobi–Isaacs equation the control law is derived. The discrete control law is then applied to a continuous-time 6-DoF bipedal robot model in order to track the walking pattern references for each link. The system along with the control law is simulated, with the system subjected to an external disturbance that emulates the action of a group of unknown bounded forces over the links of the bipedal robot. Furthermore, an algorithm to diminish the effect of the disturbance is proposed such that the full knowledge of the plant is not needed but only the linear part of the mass and inertia matrix; this algorithm is combined with the H∞ controller and applied to a robotic arm. Finally, this work is compared to a similar approach that uses H∞ technique in continuous time.

Robust compound control of dynamic bipedal robots

This paper presents a robust compound control strategy to produce a stable gait in dynamic bipedal robots under random perturbations. The proposed control strategy consists of two interactive loops: an adaptive trajectory generator and a robust trajectory tracking controller. The adaptive trajectory generator produces references for the robot controlled joints without a-priori knowledge of the terrain features and minimizes the effects of disturbances and model uncertainties during the gait, particularly during the support-leg exchange. The trajectory tracking controller is a non-switching robust multivariable generalized proportional integral (GPI) controller. The GPI controller rejects external disturbances and uncertainties faced by the robot during the swing walking phase. The proposed control strategy was evaluated on the numerical model of a five-link planar bipedal robot with one degree of under-actuation, four actuators, and point feet. The results showed robust performance and stability under external disturbances and model parameter uncertainties on uneven terrain with uphills and downhills. The stability of the gait was proven through the computation of a Poincaré return map for a hybrid zero dynamics with uncertainties (HZDU) model, which shows convergence to a bounded neighborhood of a nominal orbital periodic behavior.

Fuzzy control of bipedal running with variable speed and apex height

In this paper we propose a fuzzy-based control scheme to generate stable planar biped running gaits with variable apex height and velocity. The considered biped robot model includes five links with locked torso angles, point feet, and four actuators at the hip and knees. The controller includes two separate levels: upper-level and lower-level. The lower-level part is composed of a state machine, where the trajectory of running sub-phases and their switching time are controlled. The upper-level part includes an event-based fuzzy logic controller that is called at the apex of each flight phase. We use an offline fuzzy training process for designing fuzzy rules before controlling the robot. Fuzzy training is an iterative computational process that is repeated until convergence. Outputs of the fuzzy controller are fed into the state machine to control the running gaits. Simulation results show that the proposed control strategy generates stable gaits with controllable apex height and velocity in each step. Finally, the effects of apex height and velocity in running efficiency are investigated and optimum height is calculated as a function of running velocity.

A novel online gait optimization approach for biped robots with point-feet

Designing a stable walking gait for biped robots with point-feet is stated as a constrained nonlinear optimization problem which is normally solved by an offline numerical optimization method. On the result of an unknown modeling error or environment change, the designed gait may be ineffective and an online gait improvement is impossible after the optimization. In this paper, we apply Generalized Path Integral Stochastic Optimal Control to closed-loop model of planar biped robots with point-feet which leads to an online Reinforcement Learning algorithm to design the walking gait. We study the ability of the proposed method to adapt the controller of RABBIT, which is a planar biped robot with point-feet, for stable walking. The simulation results show that the method, starting a dynamically unstable initial gait, quickly compensates the modeling error and reaches to a walking with exponential stability and desired features in a new situation which was impossible by the past methods.

Motion Planning for Bipedal Robot to Perform Jump Maneuver

The remarkable ability of humans to perform jump maneuvers greatly contributes to the improvements of the obstacle negotiation ability of humans. The paper proposes a jumping control scheme for a bipedal robot to perform a high jump. The half-body of the robot is modeled as three planar links and the motion during the launching phase is taken into account. A geometrically simple motion was first conducted through which the gear reduction ratio that matches the maximum motor output for high jumping was selected. Then, the following strategies to further exploit the motor output performance was examined: (1) to set the maximum torque of each joint as the baseline that is explicitly modeled as a piecewise linear function dependent on the joint angular velocity; (2) to exert it with a correction of the joint angular accelerations in order to satisfy some balancing criteria during the motion. The criteria include the location of ZMP (zero moment point) and the torque limit. Using the technique described above, the jumping pattern is pre-calculated to maximize the jump height. Finally, the effectiveness of the proposed method is evaluated through simulations. In the simulation, the bipedal robot model achieved a 0.477-m high jump.

Tracking Control for Electromechanical Systems Using Robust Discrete Time H∞

In this work we propose a robust controller to do tracking using the sub-optimal H∞technique with the approach of differential game theory. The problem is solved in two steps using the Block Control technique. The controller is designed in discrete time and it is synthesized for electromechanical systems which are modeled by means of the Euler-Lagrange formulation. Making use of the discrete Hamilton-Jacobi-Isaacs equation and the discrete Riccati equation the control law is derived. The control law is then applied to a continuous-time 6-DOF bipedal robot model in order to track the walking pattern references for each link. The system along with the control law is simulated, where the system is subjected to a disturbance that emulates the action of a group of external unknown bounded forces over the links of the bipedal robot. The simulation results are shown displaying robustness against the disturbance, torques required from the motors are plot and since the control input was optimized the values lie within a reasonable bound. Furthermore, this work is compared to a similar approach that uses H∞ technique in continuous time.

A procedure to find equivalences among dynamic models of planar biped robots

In this paper, a method to find equivalences among dynamic models is presented. The models are given in different generalized coordinates for the same mechanical system. This novel method is valid for planar biped robots, i.e., those whose motions are executed only in a plane. We show that no matter which generalized coordinates are used to get the dynamic models, there is always an equivalence among them by using a particular input matrix. We exhibit some advantages of getting the dynamic model using absolute coordinates instead of relative coordinates, and we show how to calculate the input matrix for getting the equivalence between these models. Because of its simplicity, a compass-like biped robot model is used as example to explain in detail the novel procedure. In order to appreciate the benefits of the proposed procedure in biped robots of high degrees of freedom, we also present the equivalence between two dynamic models for the single support phase of a 5 degrees of freedom biped robot using absolute coordinates and relative ones.

Optimal three-dimensional biped walking pattern generation based on geodesics

The innovative three-dimensional humanoid biped gait planning method using geodesics is introduced in this article. In order to control three-dimensional walking, the three-dimensional linear inverted pendulum model is studied in our energy-optimal gait planning based on geodesics. The kinetic energy of the three-dimensional linear inverted pendulum model is calculated at first. Based on this kinetic energy model, the Riemannian metric is defined and the Riemannian surface is further determined by this Riemannian metric. The geodesic is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the center of gravity because the kinetic energy along the geodesic is invariant according to the geometric property of geodesics and the walking is energy-saving. Finally, a simulation experiment using a 12-degree-of-freedom biped robot model is implemented. The gait sequences of the simulated RoboErectus humanoid robot are obtained in the ROS (Robot Operating System) Gazebo environment. The proposed geodesics approach is compared with the traditional sinusoidal interpolation method by analyzing the torque feedback of each joint of both legs, and our geodesics optimization gait planning method for three-dimensional linear inverted pendulum model walking control is verified by the assessment results.