Stable force control and contact transition of a single link flexible robot using a fractional-order controller

The control of robots that interact with the environment is an open area of research. Two applications that benefit from this study are: the control of the force exerted by a robot on an object, which allows the robot to perform complex tasks like assembly operations, and the control of collisions, which allows the robot safely collaborate with humans. Robot control is difficult in these cases because: (1) bouncing between free and constrained motion appears that may cause instability, (2) switching between free motion (position) controller and constrained motion (force) controller is required being the switching instants difficult to know and (3) robot control must be robust since the mechanical impedance of the environment is unknown. Robots with flexible links may alleviate these drawbacks. Previous research on flexible robots proved stability of a PD controller that fed back the motor position when contacting an unknown environment, but force control was not achieved. This paper proposes a control system that combines a fractional-order D tip position controller with a feedforward force control. It attains higher stability robustness and higher phase margin than a PD controller, which is the integer-order controller of similar complexity. This controller outperforms previous controllers: (1) it achieves force control with nearly zero steady state error, (2) this control is robust to uncertainties in the environment and motor friction, (3) it guarantees stability (like others) but it also guarantees a higher value of the phase margin, i.e., a higher damping, and a more efficient vibration cancellation, and (4) it effectively removes bouncing. Experimental results prove the effectiveness of this new controller.

Robust Cooperative Control of Two Two-Link Flexible Manipulators on the Basis of Quasi-Static Equations

In this paper, a dynamic model of a distributed parameter system and a control architecture are developed for the closed-chain motion of two two-link flexible manipulators holding a common rigid object in a horizontal workspace. We derive the dynamic relation of deformation of the flexible links, constraint force, and rigid-object dynamics. Use of the quasi-static relation of the deformation, the constraint force, and the rigid-object dynamics gives quasi-static equations of joint angles which are not dependent on the variables related to the deformations of the flexible links. We design a robust cooperative controller of the two flexible manipulators considering measurement disturbances and modeling errors caused by the link-parameter uncertainty and the quasi-static approximation. A set of experiments for the cooperative control of the two flexible manipulators using a force sensor has been carried out. Several experimental results are shown.

Tip-contact force control of a single-link flexible arm using feedback and parallel compensation approach

In this paper, the force control of a constrained one-link flexible arm is investigated using a feedback parallel compensation algorithm based on a linear distributed parameter model with internal damping of Kelvin–Voigt type. Generally, the non-collocation of the joint torque input and the tip contact force output comes along with the non-minimum phase in nature. To overcome this inherent limitation, a new input induced by the measurement of root-bending moment and its derivative, and a virtual contact force output generated by a parallel compensator are defined. Therefore, the transfer function from the new input to the virtual contact force output is proved not only strictly minimum phase but also in a stable condition. A PD controller then improves the performance of the overall closed-loop system. Furthermore, the perfect asymptotic tracking of a desired contact force trajectory with internal stability can be achieved accurately. The exact solutions of the infinite-dimensional system are obtained using the infinite product formulation. The proposed system promises stability robustness to parameter uncertainties, also free of spillover problems. Numerical simulations are provided to verify the effectiveness of the proposed approach.

Expansion of source equation of elastic line

The paper is concerned with the relationship between the equation of elastic line motion, the “Euler-Bernoulli approach” (EBA), and equation of motion at the point of elastic line tip, the “Lumped-mass approach” (LMA). The Euler–Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler–Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. This yields the difference in the structure of Euler–Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and can not be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the joint and of the link (two modes), as well the environment force dynamics.

Dynamic simulation of task constrained of a rigid-flexible manipulator

A rigid-flexible manipulator may be assigned tasks in a moving environment where the winds or vibrations affect the position and/or orientation of surface of operation. Consequently, losses of the contact and perhaps degradation of the performance may occur as references are changed. When the environment is moving, knowledge of the angle α between the contact surface and the horizontal is required at every instant. In this paper, different profiles for the time varying angle α are proposed to investigate the effect of this change into the contact force and the joint torques of a rigid-flexible manipulator. The coefficients of the equation of the proposed rotating surface are changing with time to determine the new X and Y coordinates of the moving surface as the surface rotates.