ZMP-based motion planning algorithm for kinematically redundant manipulator standing on the ground

This paper proposes an approach of generating the gait pattern that Asian Institute of Technology's Leg EXoskeleton (ALEX) and its wearer can walk safely with the passing criteria of Zero Moment Point (ZMP) theorem for static and dynamic considerations, respectively. ALEX has 12 DOF (6 DOF for each leg: 3 at the Hip, 1 at the knee and 2 at the ankle), controlled by 12 DC motors. The CAD drawing and assembly of ALEX are exported directly to MATLAB's Simulink/SimMechanics simulation environment to assure accurate positioning of center of gravity (CG) and moment of inertia of each of the links that make up this 12 DOF robot. The gait pattern is visually observed in virtual environment (VR) using 3D VRML interpreter while ZMP trajectory is monitored using MATLAB's 2D graphics representation. With this developed simulation of ALEX, the robot can be tested to confirm its balance gait motion prior to the real implementation on the physical system that could cause serious damages to the robot itself and its fragile electronic devices.

In this paper, we address the problem of gait generation for bipedal robots. We cast the determination of a Center of Mass (CoM) reference trajectory for a given Zero Moment Point (ZMP) desired behaviour as a stable inversion problem for non-minimum phase systems and obtain an analytical solution for any given ZMP trajectory. Our method exploits results from our previous research, in which we derived a family of bounded CoM trajectories associated to a given desired ZMP trajectory.

This paper presents a trajectory generation approach for a 7-DOF biped robot on level ground. Simultaneously rotation of feet in double support phase is considered which leads to high-speed and more similar to human being walking. The zero moment point (ZMP) stability criterion is used to ensure the stability of the bipedal walking robot. Since ZMP trajectory in human walking does not stay fixed, it needs to be a straight line shaped forward ZMP trajectory to have a natural walk. A genetic algorithm based method is proposed to obtain key parameters in trajectory generation such that the ZMP follows a predefined trajectory while minimizing power consumption. Simulation results demonstrate the effectiveness of the proposed method.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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. Linear Inverted Pendulum Model (LIPM) and Zero Moment Point (ZMP) Criterion-based approaches in stable walking reference generation are reported. In these methods, generally, 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 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. A simple inverse kinematics-based joint space controller is used for the tests of the developed reference trajectory through full-dynamics 3-D simulation. A 12-DOF biped robot model is used in the simulations. Simulation studies suggest that the moving ZMP references are more energy efficient than the ones with fixed ZMP under the supporting foot. The results are promising for implementations. </para>

The paper presents a new method for generating the desired gaits in biped robot based on the reactive force between the feet and ground. The relation between the reactive force and joint motion is derived using the D'Almbert principle. In view of stale walking, the zero moment point (ZMP) stability criterion must be included in the desired gait generation. The proposed method utilizes aforesaid relation and stability principle to generate the desired joint trajectories. Meanwhile, desired motion trajectories and desired ZMP trajectories are also considered. The desired trajectory of the ZMP is determined by a fuzzy logic based on the human locomotion. The proposed method can reduce the motion range of the trunk, and can be applied to both the single foot supporting phase and double feet supporting phase by changing the restraining condition to the swinging leg.

Humanoid robot is the most intimate robot platform suitable for human interaction and services. Biped walking is its basic locomotion method, which is performed with combination of joint actuator's rotations in the lower extremity. The present work employs humanoid robot simulator and numerical optimization method to generate optimal joint trajectories for biped walking. The simulator is developed with Matlab based on the robot structure constructed with the Denavit-Hartenberg (DH) convention. Particle swarm optimization method minimizes the cost function for biped walking associated with performance index such as altitude trajectory of clearance foot and stability index concerning zero moment point (ZMP) trajectory. In this paper, instead of checking whether ZMP's position is inside the stable region or not, reference ZMP trajectory is approximately configured with feature points by which piece-wise linear trajectory can be drawn, and difference of reference ZMP and actual one at each sampling time is added to the cost function. The optimized joint trajectories realize three phases of stable gait including initial, periodic, and final steps. For validation of the proposed approach, a small-sized humanoid robot named DARwIn-OP is commanded to walk with the optimized joint trajectories, and the walking result is successful.

The underwater vehicle-manipulator system (UVMS) is basically a redundant system. Hence, this redundant system can have various combinations of joint velocities that do not affect the given velocity profile of an end-effector and this may induce a self-motion of a vehicle. In the current paper, the performance index based on the concept of Zero Moment Point(ZMP) is proposed to enhance the stability of the redundant UVMS while the specified task is performed by using the underwater manipulator. In order to generate the joint angle trajectories of the manipulator, a redundancy resolution is performed to minimize the distance between the position of ZMP and the mass center of the underwater vehicle, which means the propulsion energy for controlling the vehicle's motion can be reduced. To control the motion of the system with uncertainties, a controller based on the sliding mode theory has been designed. Finally, an example simulation of a simple UVMS is conducted to show the performance of the designed robust controller.

Linear Inverted Pendulum model (LIPM) is a classical theory of biped robot gait planning. However, the fixed Zero Moment Point (ZMP) of each step does not conform to the laws of human motion. In this paper, we proposed a VSP-based gait planning algorithm to make the ZMP trajectory comply the law of Heel to Toe and smooth the velocity of the center of mass (CoM). We found it remarkable that combining Virtual Supporting Point (VSP) with classical LIPM increases gait stability. The simulation and hardware experimental results on THU-Walker Platform strongly verified our algorithm.

A method for position analysis of a kind of nine-link Barranov truss

Whenever bipedal robots need to make turns, the ability to walk stably and precisely along a circular curve of an arbitrary radius will be quite beneficial. This motivates us to derive new Zero Moment Point (ZMP) constraint equations with respect to a rotating coordinate frame, seek appropriate dynamic gaits based on them, and address the forward and inverse kinematics. After the relevant body and feet trajectories are fully prescribed, joint motions are determined using the inverse kinematics. A set of dynamic walking patterns including the transient are herein proposed and applied to an exemplificative case of turning locomotion. Conclusively, dynamic simulations prove the patterns to be successful even in the presence of distributed-mass and ground contact effects.

A planar mechanical library in the AMESim simulation software. Part I: Formulation of dynamics equations

&lt;div class="htmlview paragraph"&gt;A method to simulate digital human running using an optimization-based approach is presented. The digital human is considered as a mechanical system that includes link lengths, mass moments of inertia, joint torques, and external forces. The problem is formulated as an optimization problem to determine the joint angle profiles. The kinematics analysis of the model is carried out using the Denavit-Hartenberg method. The B-spline approximation is used for discretization of the joint angle profiles, and the recursive formulation is used for the dynamic equilibrium analysis. The equations of motion thus obtained are treated as equality constraints in the optimization process. With this formulation, a method for the integration of constrained equations of motion is not required. This is a unique feature of the present formulation and has advantages for the numerical solution process. The formulation also offers considerable flexibility for simulating different running conditions quite routinely. The zero moment point (ZMP) constraint during the foot support phase is imposed in the optimization problem. The proposed approach works quite well, and several realistic simulations of human running are generated.&lt;/div&gt;

Precise position force control is the core and difficulty of robot technology, especially for robots with redundant degrees of freedom. For example, track-based controls often fail to grind the robot due to the intolerable impact force applied to the end-effector. The main difficulties lie in the coupling of motion and contact forces, redundancy analysis and physical constraints. In this chapter, we propose a new motion force control strategy under the framework of recursive neural network. The tracking error and contact force are described respectively in the orthogonal space. By choosing the minimum joint torque as the secondary task, the control problem is transformed into the QP problem under multi-constraint conditions. In order to obtain real-time optimization of the joint torque relative to the non-convex joint angle, the original QP is reconstructed at the velocity level, and the original objective function is replaced by the time derivative. Then a convergent dynamic neural network is established to solve the improved QP problem online. The robot position control based on recursive neural network is extended to the robot position control based on position force, which opens a new way for the robot to turn from simple control angle to crossover design with convergence and optimality. Numerical results show that the proposed method can realize precise position force control, deal with inequality constraints such as joint angular velocity and torque limitation, and reduce joint torque consumption by 16% on average.

In this paper a zero moment point (ZMP) trajectory of a humanoid robot model, Surena II, is presented. Humanoid stability is controlled by a PID and a fuzzy controller at two conditions, with and without the presence of external disturbance. Dynamic modeling and control implementation is performed simultaneously in the simulation. The angles of joints are set by offline method, unless the waist angle, which is the control joint and its amplitude is set by the controllers.

Demands have been increasing for skillful robots in many fields including atomic power generation, ocean bottom development, space craft, hospital aids, and so on. Such robots will essentially require high degrees of freedom. This paper discusses the advantages of a robot equipped with redundant degrees of freedom and outlines a method of positive use of such redundancy.