An inverted pendulum based approach to biped trajectory generation with swing leg dynamics (original) (raw)
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Quasi-inverse pendulum model of 12 DoF bipedal walking
International Journal of Automation and Computing, 2017
This paper presents modeling of a 12-degree of freedom (DoF) bipedal robot, focusing on the lower limbs of the system, and trajectory design for walking on straight path. Gait trajectories are designed by modeling of center of mass (CoM) trajectory and swing foot ankle trajectory based on stance foot ankle. The dynamic equations of motion of the bipedal robot are derived by considering the system as a quasi inverted pendulum (QIP) model. The direction and acceleration of CoM movement of the QIP model is determined by the position of CoM relative to the centre of pressure (CoP). To determine heel-contact and toe-off, two custom designed switches are attached with heel and toe positions of each foot. Four force sensitive resistor (FSR) sensors are also placed at the plantar surface to measure pressure that is induced on each foot while walking which leads to the calculation of CoP trajectory. The paper also describes forward kinematic (FK) and inverse kinematic (IK) investigations of the biped model where Denavit-Hartenberg (D-H) representation and Geometric-Trigonometric (G-T) formulation approach are applied. Experiments are carried out to ensure the reliability of the proposed model where the links of the bipedal system follow the best possible trajectories while walking on straight path.
Biped walking stabilization based on linear inverted pendulum tracking
Intelligent Robots and …
A novel framework of biped walking stabilization control is introduced. The target robot is a 42 DOF humanoid robot HRP-4C which has a body dimensions close to the average Japanese female. We develop a body posture controller and foot force controllers on the joint position servo of the robot. By applying this posture/force control, we can regard the robot system as a simple linear inverted pendulum with ZMP delay. After a preliminary experiment to confirm the linear dynamics, we design a tracking controller for walking stabilization. It is evaluated in the experiments of HRP-4C walking and turning on a lab floor. The robot can also perform an outdoor walk on an uneven pavement.
Inverse kinematics and inverse dynamics for control of a biped walking machine
Journal of Robotic Systems, 1993
Analytical techniques are presented for the motion planning and control of a 12 degreeof-freedom biped walking machine. From the Newton-Euler equations, joint torques are obtained in terms of joint trajectories, and the inverse dynamics are developed for both the single-support and double-support cases. Physical admissibility of the biped trajectory is characterized in terms of the equivalent force-moment and zero-moment point. This methodology has been used to obtain reference inputs and implement the feedforward control of walking robots. A simulation example illustrates the application of the techniques to plan the forward-walking trajectory of the biped robot. The implementation of a prototype mechanism and controller is also described. 0
BIPED HOPPING CONTROL BASED ON SPRING LOADED INVERTED PENDULUM MODEL
Int. J. Human. …, 2010
Human running can be stabilized in a wide range of speeds by automatically adjusting muscular properties of leg and torso. It is known that fast locomotion dynamics can be approximated by a spring loaded inverted pendulum (SLIP) system, in which leg is replaced by a single spring connecting body mass to ground. Taking advantage of the inherent stability of SLIP model, a hybrid control strategy is developed that guarantees a stable biped locomotion in sagittal plane. In the presented approach, nonlinear control methods are applied to synchronize the biped dynamics and the spring-mass dynamics. As the biped center of mass follows the mass of the mass-spring model, the whole biped performs a stable locomotion corresponding to SLIP model. Simulations are done to obtain a repeatable hopping for a three-link underactuated biped model. Results show that periodic hopping gaits can be stabilized, and the presented control strategy provides feasible gait trajectories for stance and swing phases.
BIPED HOPPING CONTROL BAzSED ON SPRING LOADED INVERTED PENDULUM MODEL
International Journal of Humanoid Robotics, 2010
Human running can be stabilized in a wide range of speeds by automatically adjusting 21 muscular properties of leg and torso. It is known that fast locomotion dynamics can be approximated by a spring loaded inverted pendulum (SLIP) system, in which leg is 23 replaced by a single spring connecting body mass to ground. Taking advantage of the inherent stability of SLIP model, a hybrid control strategy is developed that guarantees 25 a stable biped locomotion in sagittal plane. In the presented approach, nonlinear control methods are applied to synchronize the biped dynamics and the spring-mass dynamics.
2015 IEEE International Conference on Robotics and Automation (ICRA), 2015
Pendulum models have been studied as benchmark problems for development of nonlinear control schemes, as well as reduced-order models for the dynamics analysis of locomotion of humanoid robots. This work provides a generalization of the previously introduced Reaction Mass Pendulum (RMP), which is a multibody inverted pendulum model, to a bipedal model that can better model bipedal locomotion. The RMP consists of an extensible "leg" and a "body" with moving proof masses that give rise to a variable rotational inertia. The Reaction Mass Biped (RMB) introduced here has two legs, one of which takes the role of a stance leg and the other performs as a swing leg during bipedal locomotion. The bipedal walking dynamics model of the RMB is therefore hybrid, with the roles of stance leg and swing leg interchanged after each cycle. The dynamics model is developed using a variational mechanics approach, without using generalized coordinates for the rotational degrees of freedom. This dynamics model has thirteen degrees of freedom, all of which are considered to be actuated in the control design. A set of desired state trajectories that can enable bipedal walking in straight and curved lines are generated. A control scheme is then designed for asymptotically stable tracking of this set of trajectories with an almost global domain of attraction. Numerical simulation results confirm the stability of this tracking control scheme for different walking trajectories of the RMB.
Biped robot reference generation with natural ZMP trajectories
Humanoid robotics attracted the attention of many researchers in the past 35 years. The motivation of research is the suitability of the biped structure for tasks in the human environment. The control of a biped humanoid is a challenging task due to the hard-to-stabilize dynamics. Walking reference trajectory generation is a key problem. A criterion used for the reference generation is that the reference trajectory should be suitable to be followed by the robot with its natural dynamics with minimal control intervention. Reference generation techniques with the so-called Linear Inverted Pendulum Model (LIPM) are based on this idea. The Zero Moment Point (ZMP) Criterion is widely employed in the stability analysis of biped robot walk. Improved versions of the LIPM based reference generation obtained by applying the ZMP Criterion are reported too. In these methods, the ZMP during a stepping motion is kept fixed in the middle of the supporting foot sole. This kind of reference generation lacks naturalness, in that, the ZMP in the human walk does not stay fixed, but it moves forward, under the supporting foot. This paper proposes a reference generation algorithm based on the LIPM and moving support foot ZMP references. The application of Fourier series approximation simplifies the solution and it generates a smooth ZMP reference. Trajectory and force control methods for locomotion are devised and applied too. The developed techniques are tested through simulation with a 12 DOF biped robot model. The results obtained are promising for implementations. I.
Humanoid Gait Synthesis with Moving Single Support Zmp Trajecories
in Proc. The 13th IASTED …, 2007
The control of a biped humanoid is a difficult task due to the hard-to-stabilize dynamics. Walking reference trajectory generation is a key problem. Reference generation techniques with the so-called Linear Inverted Pendulum Model (LIPM) are reported. Improved versions of the LIPM based reference generation are obtained by applying the Zero Moment Point (ZMP) Criterion, widely employed in the stability analysis of biped robot walk. Typically, the ZMP reference during a stepping motion is kept fixed in the middle of the supporting foot sole. This kind of reference generation lacks naturalness, in that, the ZMP in the human walk does not stay fixed, but it moves under the supporting foot. This paper proposes a reference generation algorithm based on single support foot ZMP references which move in directions parallel and perpendicular to the walking direction. A simple inverse kinematics based independent joint position controller is used in the full dynamics 3-D simulations with the model of a 12 Degrees of Freedom (DOF) biped robot. Simulation studies indicate that the moving ZMP references result in a more successful walk.
Variable Inverted Pendulum Applied to Humanoid Motion Design
Robotica, 2021
SUMMARY Double inverted pendulum model, stationary or on a cart, is computationally the simplest out of the range of reasonable models used for anthropomorphic robots motion synthesis. However, it is still not sufficient for describing more complex situations. The novel concept of variable double inverted pendulum (VDIP) for static postures and VDIP on cart (VDIPC) for dynamic cases is proposed. It provides a simplified but a sufficiently accurate tool for planning the human-like static and dynamic robot postures. Its variable parameters enable the description of both human static postures and motion dynamics. The variable length of the lower link is essential for the representation of postures attained by bending legs. The studies of a set of static and dynamic postures were used for deducing and verifying the locations of lower and upper joint of a double pendulum and the point masses. To justify the concept, human body and pendulum behaviors are compared taking into account a typ...
Walking principle of bipcd robot is clarified with Z M P (Zem Moment Point) concept, friction constraint, and inverted pendulum model in this paper. The stable waking condition is derived out with ZMF' constraint, friction constraint, and inverted pendulum model. With this result, the nature tbat the biped walking is in fact a continually acceleration and deceleration motion is presented and its walking velocity can be adjusted by controlling landing point. The desired ZMP trajectory is given out based on derived stable walking condition, and the motion parameters of bipcd robot, such as waking stride, period, and their restriction are investigated. The approach used in this paper is expected to exend to analyze the motion of running and jump robot.