Linear Inverted Pendulum Mode Research Articles

A continuous-time walking pattern generator for realizing seamless transition between flat-contact and heel-to-toe walking

A planning algorithm that can generate continuous-time walking patterns including the seamless transition between flat-contact and heel-to-toe walking gaits is proposed. The planner makes use of the closed-form solution of a modified linear inverted pendulum mode which includes the ZMP and the weight ratio of each foot explicitly in its dynamics. The heel-to-toe movement of each foot is directly parameterized by the ZMP, and therefore consistency between the foot movement and the low-dimensional dynamics is ensured. In simulations with a 32 DoF model of a life-sized humanoid robot, fast human-like walking at the maximum speed of 4.6 km/h was achieved.

Humanoid Loco-Manipulations Pattern Generation and Stabilization Control

In order for a humanoid robot to perform loco-manipulation such as moving an object while walking, it is necessary to account for sustained or alternating external forces other than ground-feet reaction, resulting from humanoid-object contact interactions. In this letter, we propose a bipedal control strategy for humanoid loco-manipulation that can cope with such external forces. First, the basic formulas of the bipedal dynamics, i.e., linear inverted pendulum mode and divergent component of motion, are derived, taking into account the effects of external manipulation forces. Then, we propose a pattern generator to plan center of mass trajectories consistent with the reference trajectory of the manipulation forces, and a stabilizer to compensate for the error between desired and actual manipulation forces. The effectiveness of our controller is assessed both in simulation and loco-manipulation experiments with real humanoid robots.

MODELING AND CONTROL OF HUMAN AND WHEELED ROBOTIC WALKER COUPLED DYNAMICS

The control of assistive robotic walkers are usually designed without considering the coupled dynamics of the user and the walker. This paper proposes a coupled dynamic modeling for human walking with a wheeled robotic walker and then control of this model. The 2D linear inverted pendulum mode (LIPM) is used to model human walking. The wheeled robotic walker is modeled as a simple wheeled subsystem moving on an even ground. To simulate the human arm, a parallel linear spring and damper set is then used to indicate the interaction forces. An optimal fixed final-state controller is used to control the walking model and to keep it balanced. To check whether the LIPM model walking is balanced, the zero-moment point position is calculated and checked to be in the support polygon. The results are validated with the experimental data of human walking along with a wheeled walker for three healthy subjects. The relative positions of center of mass, the absolute positions of the human and the walker, and the velocities are considered for comparison and discussion. The results for each subject is compared with the experiments through [Formula: see text] norm of the error between human and walker positions in simulation and experiments. The proposed model can be utilized in developing controllers for robotic walkers that consider the user’s dynamics.

Intelligent Control and Dynamic Modeling for System of Human and Wheeled Robotic Walker

In order to develop assistive devices that involve physical human–robot interaction, a dynamical model of the human and the robot should be considered. This paper proposes a coupled dynamic model for human walking with a wheeled robotic walker together with a built-in fuzzy controller on the human model. The 2-D linear inverted pendulum mode is used to model human walking coupled through a parallel linear spring and damper to the walker robot. In order to generate a stable walking pattern, a fuzzy controller is implemented. The controller performance is compared to a conventional PID controller, and the results are validated with the experimental data of human walking along with a wheeled walker for five healthy subjects. The proposed model can be utilized in developing controllers for robotic walkers that consider the user’s dynamics.

Energy-Efficient Gait Planning and Control for Biped Robots Utilizing the Allowable ZMP Region

Energy-efficient gait planning and control is established for biped robots, which utilizes the allowable zero moment point (ZMP) region. Based on 3-D linear inverted pendulum mode (LIPM), we construct a practical gait planning algorithm for a given travel distance minimizing the energy consumed by the actuators of humanoid joints with 1) an online gait synthesis (GSYN) algorithm to generate a complete walking cycle (a starting step, several cyclic steps, and a stopping step) compromising waking stability and energy efficiency at the fully utilizing allowable ZMP region and with 2) effective gait parameter optimization to maximize the energy efficiency of the gaits generated by GSYN, finding two optimal parameters-number of steps and average walking speed-satisfying geometrical constraints, friction force limit, and yawing moment limit to guarantee feasible motions. The proposed algorithm was verified through simulations, and the gait control system was implemented on a DARwIn-OP humanoid robot.

Observer based biped walking control, a sensor fusion approach

In humanoid walking research, the prevailing approach is to utilize an abstraction of the robot to a single center of mass (3D linear inverted pendulum mode). Smaller disturbances or an oscillation of the body are typical for a walking robot and must be addressed by an appropriate sensor feedback. To this end, this paper proposes a novel observer fusing joint angle sensors and force sensing resistors. This new method of sensor feedback in a preview control system balances the walk by damping those disturbances and oscillations of the body. Moreover, novel stabilizing methods for defining reference trajectories for the zero moment point and limbs are examined.

Backflips Performed by Humanoid Robots Based on Extended Linear Inverted Pendulum Mode

Abstract This paper proposes a method to realize a backflip motion for humanoid robots. In each phase of the backflip motion, the trajectory is planned. Besides, the Extended Linear Inverted Pendulum Mode (E-LIPM) is newly proposed to generate angular momentum that is needed for turning the body of the robot. In landing, an Impedance control is used to absorb the impact from the ground. Computer simulations of a backflip by a 7-DOF humanoid robot were performed, whose results show that the proposed method works well. This method is expected to be used for more complex motions of humanoid robots.

ELIPM을 이용한 이족보행로봇의 궤적생성

궤적생성은 로봇보행의 안정성, 연속성 그리고 보행특성을 결정하는 가장 중요한 일이다. 보통 궤적생성법으로 LIPM을 많이 쓰지만 그것은 그것의 선형화 기법 때문에 수직방향으로의 동작생성을 할 수 없다는 단점이 있다. 이 논문에서는 ELIPM이라는 새로운 궤적생성법을 제안한다. 이 궤적생성법은 전진방향의 동작은 물론이고 수직방향의 동작을 간단하게 생성할 수 있다.

이중 병렬형 다리 구조를 가진 2족보행로봇의 보행제어

본 논문은 2족 보행로봇을 위한 새로운 병렬메카니즘을 제안하고 있다. 각 다리는 3자유도를 갖는 병렬 플랫폼 2개가 시리얼로 연결되어 있는데, 허벅지와 정갱이 역할을 한다. 이 제안된 로봇을 위한 보행 궤적은 보행평면상에서는 중력보상역진자모드를 사용하여 구하였고, 횡방향으로는 역진자모드를 사용하여 구하였다. 지면으로부터의 반발력을 시뮬레이션하기 위해 발바닥 밑에 6자유도의 패드를 사용하였다. 제안된 메카니즘과 보행제어의 효율성은 SimMechanics를 이용한 12자유도 병렬 2족보행 로봇의 시뮬레이션을 통해 입증하였다.

2족 보행로봇을 위한 여유자유도 궤적 생성

A biped robot in locomotion can be regarded to be kinetically redundant in that the link-chain from its foot on the ground to its swing foot has more degrees of freedom that needed to realize stable bipedal locomotion. This paper proposes a new method to generate a trajectory for bipedal locomotion based on this redundancy, which directly generates a locomotion trajectory at the joint level unlike some other methods such as LIPM (linear inverted-pendulum mode) and GCIPM (gravity-compensated inverted-pendulum mode), each of which generates a trajectory of the center of gravity or the hip link under the assumption of the dominance of the hip-link inertia before generating the trajectory of the whole links at the joint level. For the stability of the trajectory generated in the proposed method, a stability condition based on the ZMP (zero-moment point) is used as a constraint as well as other kinetic constraints for bipedal motions. A 6-DOF biped robot is used to show how a stable locomotion trajectory can be generated in the sagittal plane by the proposed method and to demonstrate the feasibility of the proposed method.

Tip over avoidance control for biped robot

SUMMARYThis paper analyzes the stabilization problem from the energy point of view. Perturbations are detected by the gyros and categorized according to the constraints on the zero-moment point, energy, and walking pattern. Ankle torque is exerted to extend the linear inverted pendulum mode (LIPM). Compensation movement is computed according to the analysis on the energy of LIPM and the influence of disturbance to the energy. The experimental results from both the simulation and the physical robot not only proved effective but also explain various human reactions to disturbance in locomotion.

A Bipedal Locomotion Planning Based on Virtual Linear Inverted Pendulum Mode

In this paper, a bipedal locomotion planning based on virtual linear inverted pendulum mode (VLIPM) is proposed. In conventional methods, the desired center of gravity (COG) position and velocity are achieved by modifying the foot placement. In this research, the desired COG position and velocity are achieved while the desired foot placement is also realized. In the proposed method, the virtual modified foot placement and trajectory planning are calculated separately. VLIPM is applied to the calculation of the virtual modified foot placement. By using virtual supporting point (VSP), the difference between the virtual modified and desired foot placements is compensated. In the result, the desired foot placement is achieved as if the foot placement is in the virtual modified foot placement. Trajectory planning is applied to LIPM with VSP and 5-D polynomial. The boundary conditions of the polynomial are set to the desired COG position and velocity. In the result, the desired COG position and velocity are also obtained. Differences of the motion by different models are compensated by matching the boundary conditions of different models. By applying different models in the calculations of the foot placement and trajectory planning, the desired robot motion is realized. The walking stability of the proposed method is equivalent to that of the conventional method. The effectiveness of the proposed method is confirmed by a simulation and an experiment.

Modifiable Walking Pattern of a Humanoid Robot by Using Allowable ZMP Variation

In order to handle complex navigational commands, this paper proposes a novel algorithm that can modify a walking period and a step length in both sagittal and lateral planes. By allowing a variation of zero moment point (ZMP) over the convex hull of foot polygon, it is possible to change the center of mass (CM) position and velocity independently throughout the single support phase. This permits a range of dynamic walking motion, which is not achievable using the 3-D linear inverted pendulum mode (3D-LIPM). In addition, the proposed algorithm enables to determine the dynamic feasibility of desired motion via the construction of feasible region, which is explicitly computed from the current CM state with simple ZMP functions. Moreover, adopting the closed-form functions makes it possible to calculate the algorithm in real time. The effectiveness of the proposed algorithm is demonstrated through both computer simulation and experiment on the humanoid robot, HanSaRam-VII, developed at the Robot Intelligence Technology (RIT) laboratory, Korea Advanced Institute of Science and Technology (KAIST).

Collision Avoidance Method of Humanoid Robot With Arm Force

This paper describes a collision avoidance method for a biped robot with an upper body. We propose a method wherein the robot stops in front of an obstacle by generating arm force. When the robot detects the obstacle by the arm tip, it should stop short of the obstacle to avoid crash. Hence, we propose trajectory planning in consideration of the pushing force of the arm. The arm force is controlled to be generated as a function of the distance from the robot body to the obstacle. The closer the robot approaches the obstacle, the larger the arm force becomes. As a result, the robot can stop by utilizing the arm force. In case the obstacle is unmovable, the robot can stop by exerting arm force. If it is movable, the robot can continue walking by pushing it. In this paper, the linear inverted pendulum mode (LIPM) and the idea of orbital energy are introduced, and then, we extend LIPM and orbital energy in consideration of the dynamics of the arm force. The extended orbital energy is utilized to discriminate whether the robot can stop or not and to modify the trajectory of the robot to avoid collision

Biped walking pattern generation by a simple three-dimensional inverted pendulum model

For three-dimensional (3D) walking control of a biped robot we analyze the dynamics of a 3D inverted pendulum in which motion is constrained to move along an arbitrarily defined plane. This analysis leads us to a simple linear dynamics, the Three-Dimensional Linear Inverted Pendulum Mode (3D-LIPM). The geometric nature of the trajectories under the 3D-LIPM and a method for walking pattern generation are discussed. A simulation result of a walking control using a 12-d.o.f. biped robot model is also shown.

Adaptive Gait Control of a Biped Robot Based on RealtimeSensing of the Ground Profile

In this paper, realtime control of dynamic biped locomotion using sensor information is investigated. We used an ultrasonic range sensor mounted on the robot to measure the distance from the robot to the ground surface. During the walking control, the sensor data is converted into a simple representation of the ground profile in realtime. We also developed a control architecture based on the Linear Inverted Pendulum Mode which we proposed previously for dynamic walking control. Combining the sensory system and the control system enabled our biped robot, Meltran II, to walk over ground of unknown profile successfully.

Experimental study of biped dynamic walking

An experimental study of a biped robot is presented. A new scheme named the "linear inverted pendulum mode" is utilized for controlling a biped walking on rugged terrain. The authors developed a six-DOF biped robot, "Meltran II," which has lightweight legs and moves in a two-dimensional vertical plane. To investigate the effects not well discussed in the theory, the authors carried out two experiments, the support phase experiment and the support exchange experiment. The support phase experiment was carried out to check the actual dynamics of a biped walking under the proposed control. It was shown that the dynamics of the robot can be regarded as linear even though the mass of the legs, which was neglected in the theory, exists. The support exchange experiment was performed to check leg support exchange. The authors found that a smooth leg support exchange is achieved by making the foot contact with a certain vertical speed and holding two-leg support for a certain short period. Based on these results, a whole biped control system was implemented. In the authors' experiment the robot walked over a box of 3.5 cm height at a speed of 20 cm/s.

Study of Dynamic Walk Control of a Biped Robot on Rugged Terrain - Derivation and Application of the Linear Inverted Pendulum Mode -

This paper introduces a control method for biped walking on rugged terrain. We assume a biped robot which has a mass body and massless legs, and which is restricted to move in a vertical plane. We apply constrain control to the body of the robot so that it moves on a particular straight line and rotates at a constant angular velocity. As the result of such control, the dynamics of the center of mass of the body becomes completely linear. We also notice that the dynamics of the body does not depend on the slope of the line on which the center of mass of the body is constrained. We call such motion of the ideal model ""Linear Inverted pendulum Mode"". The limitation of the condition under which this method works is also discussed. After these consideration, we have developed the control scheme of the biped walking on rugged terrain. Under the control based on the linear inverted pendulum mode, walking on a particular rugged terrain is shown to be equivalent to walking on a level surface. Finally, it is shown that by using ankle torque, our method becomes robust and can be applied to a real biped robot with mass legs. This is ascertained by simulation.

凹凸路面における動的2足歩行の制御について

This paper introduces a control method for biped walking on rugged terrain. We assume a biped robot which has a mass body and massless legs, and which is restricted to move in a vertical plane. We apply constrain control to the body of the robot so that it moves on a particular straight line and rotates at a constant angular velocity. As the result of such control, the dynamics of the center of mass of the body becomes completely linear. We also notice that the dynamics of the body does not depend on the slope of the line on which the center of mass of the body is constrained. We call such motion of the ideal model “Linear Inverted Pendulum Mode”. The limitation of the condition under which this method works is also discussed.After these consideration, we develop the control scheme of the biped walking on rugged terrain. Under the control based on the linear inverted pendulum mode, walking on a particular rugged terrain is shown to be equivalent to walking on a level surface.Finally, it is shown that by using ankle torque, our method is robust and can be applied to a real biped robot with mass legs. That is ascertained by simulation.