Implicit Contact Dynamics Modeling With Explicit Inertia Matrix Representation for Real-Time, Model-Based Control in Physical Environment

Model-based control has great potential for use in real robots due to its high sampling efficiency. Nevertheless, dealing with physical contacts and generating accurate motions are inevitable for practical robot control tasks, such as precise manipulation. For a real-time, model-based approach, the difficulty of contact-rich tasks that requires precise movement lies in the fact that a model needs to accurately predict forthcoming contact events within a limited length of time rather than detect them afterward with sensors. Therefore, in this study, we investigate whether and how neural network models can learn a task-related model useful enough for model-based control, that is, a model predicting future states, including contact events. To this end, we propose a structured neural network model predicting a control (SNN-MPC) method, whose neural network architecture is designed with explicit inertia matrix representation. To train the proposed network, we develop a two-stage modeling procedure for contact-rich dynamics from a limited number of samples. As a contact-rich task, we take up a trackball manipulation task using a physical 3-DoF finger robot. The results showed that the SNN-MPC outperformed MPC with a conventional fully connected network model on the manipulation task.

Numerical Simulation of Inertia Matrix for 6 DoF Industrial Robot

The robot dynamic model is essential for the precision and reliability of robot design, motion control, and simulation. A robot inertia matrix, whose elements are coefficients of joint accelerations within the robot equations of motion, plays an important role in the robot’s control design. During robot motion, elements of the inertia matrix are functions of robot configuration (robot joint positions). To facilitate the development of process models and to make an appropriate selection of motion control algorithms, it is useful to perform numerical simulations of inertia matrix elements for different robot trajectories. In this paper, numerical simulation of inertia matrix is presented for 6 DoF industrial robot with revolute joints for the programmed robot motion. Inertia matrix is obtained from the robot dynamical model developed by using modified recursive Newton-Euler algorithm. Based on the presented simulations, variation of effective inertias and magnitude and variation of cross-coupling effects in the robot inertia matrix are examined.

Task-Space Admittance Controller with Adaptive Inertia Matrix Conditioning

Whenrobots physically interact with the environment, compliant behaviors should be imposed to prevent damages to all entities involved in the interaction. Moreover, during physical interactions, appropriate pose controllers are usually based on the robot dynamics, in which the ill-conditioning of the joint-space inertia matrix may lead to poor performance or even instability. When the control is not precise, large interaction forces may appear due to disturbed end-effector poses, resulting in unsafe interactions. To overcome these problems, we propose a task-space admittance controller in which the inertia matrix conditioning is adapted online. To this end, the control architecture consists of an admittance controller in the outer loop, which changes the reference trajectory to the robot end-effector to achieve a desired compliant behavior; and an adaptive inertia matrix conditioning controller in the inner loop to track this trajectory and improve the closed-loop performance. We evaluated the proposed architecture on a KUKA LWR4+ robot and compared it, via rigorous statistical analyses, to an architecture in which the proposed inner motion controller was replaced by two widely used ones. The admittance controller with adaptive inertia conditioning presents better performance than with a controller based on the inverse dynamics with feedback linearization, and similar results when compared to the PID controller with gravity compensation in the inner loop.

Adaptive Backstepping Attitude Control Law with L2-Gain Performance for Flexible Spacecraft

In this paper, an observer-based adaptive backstepping attitude maneuver controller (briefly, OBABC) for flexible spacecraft is presented. First, an observer is constructed to estimate the flexible modal variables. Based on the proposed observer, a backstepping control law is presented for the case where the inertia matrix is known. Further, an adaptive law is developed to estimate the unknown parameters of the inertia matrix of the flexible spacecraft. By utilizing Lyapunov theory, the proposed OBABC law can guarantee the asymptotical convergence of the closed-loop system in the presence of the external disturbance, incorporating with the L2-gain performance criterion constraint. Simulation results show that the attitude maneuver can be achieved by the proposed observer-based adaptive backstepping attitude control law.

ROBOTIC ARM COLLISION REACTION STRATEGIES FOR SAFE HUMAN–ROBOT INTERACTION WITHOUT TORQUE SENSORS

Three kinds of collision reaction strategies for increasing safety during human and robot interactions without relying on torque sensors are proposed in this paper. In the proposed algorithms, motor torque is estimated by driver current. The generalized momentum observer is used for collision detection, which does not need joints acceleration information and calculates the inverse of the inertia matrix. Three different collision reaction strategies, going away, dragging by hands and mechanical impedance developed in this paper, aim to enhance safety to humans during physical interaction with robots. For verifying the efficiency of the proposed algorithms, experiments are tested between a 1-DOF manipulator system and a human being. At last, the experiments’ results show that the proposed collision reaction algorithms are effective.

Rigid body dynamics using equimomental systems of point-masses

The inertia matrix of any rigid body is the same as the inertia matrix of some system of four point-masses. In this work, the possible disposition of these point-masses is investigated. It is found that every system of possible point-masses with the same inertia matrix can be parameterised by the elements of the orthogonal group in four-dimensional modulo-permutation of the points. It is shown that given a fixed inertia matrix, it is possible to find a system of point-masses with the same inertia matrix but where one of the points is located at some arbitrary point. It is also possible to place two point-masses on an arbitrary line or three of the points on an arbitrary plane. The possibility of placing some of the point-masses at infinity is also investigated. Applications of these ideas to rigid body dynamics are considered. The equation of motion for a rigid body is derived in terms of a system of four point-masses. These turn out to be very simple when written in a 6-vector notation.

Satellite Inertia Parameters Estimation Based on Extended Kalman Filter

The moment of inertia parameters play a critical role in assuring the spacecraft mission throughout its lifetime. However, determination of the moment of inertia is a key challenge in operating satellites. During satellite mission, those parameters can change in orbit for many reasons such as sloshing, fuel consumption, etc. Therefore, the inertia matrix should be estimated in orbit to enhance the attitude estimation and control accuracy. This paper investigates the use of gyroscope to estimate the attitude rate and inertia matrix for low earth orbit satellite via extended Kalman filter. Simulation results show the effectiveness and advantages of the proposed algorithm in estimating these parameters without knowing the nominal inertia. The robustness of the proposed algorithm has been validated using the Monte-Carlo method. The obtained results demonstrate that the accuracy of the estimated inertia and angular velocity parameters is satisfactory for satellite with coarse accuracy mission requirements. The proposed method can be used for different types of satellites.