Kinodynamic Model Identification: A Unified Geometric Approach

All countries in the world today have different degrees of aging. In order to help the elderly to walk properly, based on the analysis about the common walking stick, this paper have developed a smart walking stick robot which meets the walking habits of the elderly. The walking stick's use process is divided into supporting state and non-support state. By analyzing the variation of force, moment and angle between users and common walking stick under two conditions, the walking stick's mathematical model is established. By analyzing the structure and movement process of the walking stick robot, a dynamic model of the robot is established. At the same time, the admittance control model is used to satisfy the suppleness of the force by controlling the chassis motion of the robot. The final design experiment verified the validity of the walking stick model and the adequacy of admittance control.

This paper presents a dynamic model of a unicycle robot which consists of a wheel and two momentum wheels. However, the dynamic model of the unicycle robot built in this paper is non-linear. By expanding the non-linear items in Taylor series around an equilibrium point, the non-linear dynamic model of the unicycle robot is linearized. And the linearized dynamic model of the unicycle robot is simplified into state equation. Based on the linearized state equation, a state feedback algorithm is designed to maintain postural stability of the unicycle robot. After completing the postural stability control algorithm, a simulation model is developed using Simulink. The capability and performance of the algorithm is verified.

A kind of two-wheeled robot is researched in this paper. Firstly, the structure is analyzed. Then, the Lagrange equations are used to make the dynamic model of the two-wheeled robot. The parameter identification experiment is based on the dynamic model of the two-wheel robot, which the genetic algorithm and the least square method are used in. The system parameters obtained through experiments was compared with those parameters obtained from the simulation using SolidWorks. The dynamic modeling was proved to be correct from the result of the experiments mentioned above.

Based on the motion analysis,the integral dynamics model of the BYQ-3 spherical robot is introduced through the Kane equation modeling method with the characteristics of vector operation,and the simulation and experiment research are implemented. The angular velocity,angular acceleration,centroid velocity and acceleration of the spherical shell,framework and weight pendulum are defined,respectively,and the generalized rate,partial velocity,partial acceleration,generalized inertial force and generalized active force of the spherical shell,framework and weight pendulum are derived,respectively. Then,the integral dynamics model of the BYQ-3 spherical robot is proposed on the basis of derived formula above. The integral dynamics model is revised through the designed model of the moment of friction torque of the rotating joint and the couple moment of rolling torque between the ground and the spherical shell. In conditions of the line motion of which the longitude axis is parallel with the ground,the simulation is presented on the basis of revised integral dynamics model,and moreover,the open motion control experiment is also presented by using the BYQ-3 spherical robot. The results of the simulation and experiment show that considering the frication factors among the system,the integral dynamics model of the BYQ-3 spherical robot is effective.

To obtain higher performance for an industrial hybrid robot, the dynamic control method is utilized to control the robot. For dynamic control, the control performance is directly affected by the accuracy of the dynamic model. This paper investigated a method to establish and identify an accurate dynamic model. First, based on the Lagrangian dynamic equation and the Stribeck friction model, the unidentified dynamic model of the five-DOF hybrid robot is established. Second, identification experiments are carried out. Each of the driving joints performs frequent reciprocating motions individually. In the meantime, the moving speed is gradually increased to obtain driving torques of the respective joint at different moving speeds. Then the dynamic parameters with lower coupling are identified by using the standard deviation index and the least squares methods until all parameters are gradually determined. Finally, the hybrid robot moves a typical trajectory, while the currents of each joint are collected to obtain the driving forces. The actual driving forces, the identified dynamic model, and the unidentified dynamic model are compared. The results show that the identified method could significantly improve the accuracy of the dynamic model. The method proposed in this paper is general and can be applied to the other robots without adding any sensors.

A walking robot consisting of double Stewarts parallel legs was designed by our research team in the past time, which was mainly used for the transportation of the wounded after the disaster. In order to promote stability of control locomotion and ensure invariably horizontal state of the robot platform in the process of motion, the central pattern generator (CPG) based on particle swarm optimization (PSO) is presented to optimize the kinematic model. The purpose of optimization is to solve the hysteresis problem of displacement variation among the electric cylinders. Moreover, the dynamic model of the robot is established, which can provide mechanical basis for the feedback of control signal and make the robot move stably. The simulation results show that the displacement hysteresis problem of the electric cylinders is solved well. Meanwhile, compared with simulation results based on GA-CPG method, it is demonstrated that the robot motion planned using PSO-CPG method has better motion stability and can avoid the impact of legs landing during the transition phase of the motion cycle. The experimental results show that the platform on the robot can maintain an invariably horizontal state, and the locomotion is more stable. It verifies the feasibility of PSO-CPG model and the correctness of the dynamic model of the parallel mobile rescue robot.

This paper proposes a unified robust motion controller for the position and force control problems of compliant robot manipulators driven by Series Elastic Actuators (SEAs). It is shown that the dynamic model of the compliant robot includes not only matched but also mismatched disturbances that act on the system through a different channel from the control input. To tackle this complex robust control problem, the unified robust motion controller is synthesised by employing a second-order Disturbance Observer (DOb), which allows us to estimate not only disturbances but also their first and second order derivatives, and a novel controller design approach in state space. By using the Brunovsky canonical form transformation and the estimations of disturbances and their first and second order derivatives, the dynamic model of the robot is reconstructed so that a new system model that includes only matched disturbances is obtained for compliant robots driven by SEAs. The robust position and force controllers are simply designed by eliminating the matched disturbances of the reconstructed system model via the conventional DOb-based robust control method. The stability and performance of the proposed robust motion controllers are verified by simulations.

Kinematic parameters’ calibration is a powerful method to improve the accuracy of the robot. This paper proposes an effective kinematic self-calibration method for dual-manipulators based on virtual constraints to estimate the actual kinematic parameters of the robots. This method only needs a camera mounted on one robot end-effector (EE) and a calibration target attached to another robot EE. First, a new calibration error model based on the straight line constraint is established to formulate the positions’ misalignment error with the kinematic parameters’ error. Then, the particle swarm optimization algorithm is developed to generate the optimal calibration poses of the robots under the constraints, which are used to ensure the poses feasible and the measurement errors acceptable. Finally, the kinematic parameter errors are identified with the Levenberg–Marquardt algorithm. The experiments of the kinematic parameters’ calibration with the dual-manipulators system are designed. The experimental results showed that the high positional accuracy of both robots can be achieved.

Kinematics and dynamic model are the foundation for system design and performance analysis, and are also the guarantee of controller practicability. The Kinematics and dynamic model of three-wheeled robot with two wheels driving are established in this paper. Three wheeled supporting structure is simple, but stability is relatively poor. So on two aspects structure optimization of the robot is completed to ensure support stability and movement flexibility.

This paper presents a high precision modeling approach for a multi-axis robot considering interference force between axes based on a dynamic model of a multi-axis robot. It is well-known that interference force affects positioning performance especially in high speed positioning motion. In order to overcome the problem, it needs a high precision model which can reproduce actual motion of a multi-axis robot. In this paper, a combined modeling approach which consists of a two-mass model and a dynamic model is proposed, where each axis is basically modeled as a two-mass model to reproduce mechanical vibrations due to elastic mechanism of the reduction gear. Interference force between axes is theoretically modeled based on a dynamic model of a multi-axis robot. The inertial term of interference force is added as disturbance at motor-side, while the velocity term of interference force and gravity force are added as disturbance at load-side. The effectiveness of the proposed modeling approach has been verified based on a comparative study with a conventional model approach based on a two-mass model only.

Task-space cooperative tracking control of the networked multiple Euler–Lagrange systems is studied in this paper. On the basis of establishing kinematic and dynamic modeling of a Euler–Lagrange system, an innovative task-space coordination controller is designed to deal with the time-varying communicating delays and uncertainties. First, in order to weaken the influence of the uncertainty of kinematic and dynamic parameters on the control error of the system, the product of the Jacobian matrix and the generalized spatial velocity are linearly parameterized; thus, the unknown parameters are separated from known parameters. The online estimation of uncertain parameters is realized by designing parameters and by proposing new adaptive laws for the dynamic and kinematic parameters. Furthermore, to describe the transmission of time-varying delay errors among networked agents, a new error term is introduced, obtained by adding the observation error and tracking error, and the coefficient of the network mutual coupling term related to the time-varying delay rate is added with reference to the generalized space velocity and task-space velocity of the Lagrange systems. In the end, the influence of the time-varying delay on the cooperative tracking control error of the networked multiple Euler–Lagrange systems is eliminated. With the help of Lyapunov stability theory, the tracking errors and synchronization errors of this system are calculated by introducing the Lyapunov–Krasovskii functional; the asymptotic convergence results rigorously prove the stability of the adaptive cooperative control systems. The simulation results verify the excellent performance of the controller.

Two dynamic models of robots with elastic hinges are considered. Dynamic models are the implementation of the method based on the Lagrange equation using the transformation matrices of elastic coordinates. Dynamic models make it possible to determine the elastic deviations from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. One model is the exact implementation of the Lagrange method and makes it possible to determine the total elastic deviation of the robot from the programmed motion trajectory. Another dynamic model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by two models are compared to the example of a two-link manipulator system. The considered models can be used when performing investigations of the mathematical accuracy of the robots.

Dynamic modeling and vibration prediction of an industrial robot in manufacturing

Despite their well-known advantages in terms of higher intrinsic rigidity, larger payload-to-weight ratio, and higher velocity and acceleration capacities, parallel robots have drawbacks. Among them, the most important one is surely the presence of singularities in the workspace, which divide the workspace into different aspects (each aspect corresponding to one or more assembly modes) and near which the performance is considerably reduced. In order to increase the reachable workspace of parallel robots, a promising solution consists in the definition of optimal trajectories passing through the singularities to change either the leg working modes or the robot assembly modes. Previous works on the field have shown that it is possible to define optimal trajectories that allow the passing through the robot type 2 singularities. Such trajectories must respect a physical criterion that can be obtained through the analysis of the degeneracy conditions of the parallel robot inverse dynamic model. However, the mentioned works were not complete: they lacked a degeneracy condition of the parallel robot inverse dynamic model, which is not due to type 2 singularity anymore, but to a serial singularity. Crossing a serial singularity is appealing as in that case we can change the robot leg working mode and then potentially access to other workspace zones. This absence is due to the fact that the authors used a reduced dynamic model, which was not taking into account all link dynamic parameters. The present paper aims to fill this gap by providing a complete study of the degeneracy conditions of the parallel robot dynamic model and by demonstrating that it is possible to cross the type 2, but also serial singularity, by defining trajectories that respect some given criteria obtained from the analysis of the degeneracy of the robot dynamic model. It also aims to demonstrate that the serial singularities have impacts on the robot effort transmission, which is a point that is usually bypassed in the literature. All theoretical developments are validated through simulations and experiments.

This paper presents dynamics modeling of a Delta robot with three revolute legs and a telescopic rod. Firstly, two generalized coordinate systems are established to describe the relationship between the movement of the telescopic rod and the position of the moving platform, and the telescopic rod system kinematics are established through singularity analysis. Secondly, taking the telescopic rod as the research object, the corresponding dynamics model is established using the Euler–Lagrange method. Moreover, this paper proposes a method to convert the force exerted by the telescopic rod motion on the moving platform into actuator torques. Thirdly, the dynamics model of the Delta robot with a telescopic rod is established, and numerical simulations are performed to demonstrate this approach. Finally, the influence of the telescopic rod on the actuator torques is verified using an experiment. A comparison is drawn between the two dynamics models used in torque feedforward control to validate the proposed dynamics model.