Elsevier

ISA Transactions

Volume 89, June 2019, Pages 139-157
ISA Transactions

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

https://doi.org/10.1016/j.isatra.2018.12.031Get rights and content

Highlights

  • New results on the force control of a single-link flexible manipulator, which is of interest in several robotic applications.

  • A fractional-order controller combined with a collision detection mechanism has been designed and implemented.

  • This methodology combines the obtention of a fractional-order robust controller to cope with unknown environment mechanical impedance.

  • Experimental validation of the proposed methodology.

Abstract

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.

Introduction

The efficient control of the interaction of robots with the environment broadens the range of application of robotics. Two applications that are benefited from this are: force control, which allows the robot to perform complex tasks like assembly operations, and collision control, which allows the robot to safely collaborate with humans.

The control of a robot interacting with the environment is difficult because: (1) bouncing between free and constrained motion appears that may cause instability, (2) switching between a free motion (position) controller and a constrained motion (force) controller is required being the switching instants difficult to obtain, and (3) robot control must be robust since the mechanical impedance of the environment is unknown.

Flexible robots are characterized by having at least one flexible element in its mechanical configuration. Flexible links are mostly utilized because they allow for robot designs with reduced weight, which involves some significant advantages over standard rigid robots: a lightweight flexible robot can perform faster movements than its equivalent in dimensions rigid counterpart, it is more easily transportable, its energy consumption is lower, and its payload-to-arm weight ratio is higher (see e.g. [1]).

Interaction with the environment is better dealt by flexible robots than by standard rigid robots, e.g., in force control tasks [2] or in cooperative tasks with humans [3]. The following advantages can be ascertained in the case of flexible link robots:

  • 1.

    When a rigid robot and a rigid object collide, the contact force grows very quickly (in μs), reaching a very high value before the control system acknowledges the contact. Then, the object or a robot component may be broken. When a flexible link collides, instead, part of its kinetic energy is gradually transformed into link elastic potential energy. The contact force grows then more slowly (in ms) and the control system can timely detect the impact and switch from position to force control, reducing the harming effects of the impact.

  • 2.

    When a rigid robot performs tasks involving contact with the environment, like assemblies, small errors in the robot end effector position yield high contact forces that often impede the execution. This is overcome using complex sensory systems, computer-aided design models of the environment and complex task planning systems. Instead, flexible link robots absorb these errors by slightly deforming their links, yielding moderate values of the contact force that facilitate these tasks. This deflecting feature has been exploited in industry, in which compliant mechanisms are inserted at certain points of the robot to achieve assembly tasks, e.g., the Remote Center of Compliance Device  [4].

  • 3.

    Impedance control is a useful technique that combinesposition–force control in robotics [5], being quite stable in transitions from free to constrained movements. It can be easily implemented using robots with flexible links, in which part of the impedance control is passively performed by the compliant structure of the robot.

  • 4.

    Damage on an operator of the impact of a robot would be drastically reduced. For example, the head injury criterion HIC [3], [6] is defined as: HIC=22π32KcovMoper34MrobMrob+Moper74vrob52where vrob is the speed of the robot, Mrob is the mass of the robot, Moper is the mass of the impacted operator, and Kcov is the lumped stiffness of a compliant cover on the arm (in our case, it is assimilated to the compliance of the flexible link). HIC index is much smaller in a flexible link robot than in a rigid one because Mrob and Kcov are smaller. Moreover, control systems can be designed taking into account previous issues (1) to (3) to further reduce collision harm.

However, undesired vibrations and deflections appear in the structure of flexible link robots that make their control significantly complicate. A survey on free motion control techniques of these robots is [7].

Several strategies were proposed to control rigid robots interacting with the environment. They can be grouped into impedance control [8] and hybrid position–force control [9], and have also been extended to flexible robots. Examples for robots with two flexible links are impedance control [10] and hybrid position–force control [11].

Research has been carried out on contact detection mechanisms for rigid robots [12], [13] and flexible link robots [14]. Thresholds of some functions of generalized robot momenta and motor torques were used to trigger the change of the control law. In these control systems, after the contact had been detected, the robot was stopped in a position in which no contact was established with the object (preventing harming a person) or in a position in which some force was exerted on a soft object. In all these cases, rebounds were minimum and did not deteriorate the control performance.

Control of rigid robots interacting with the environment has been proposed, that switches from position to force control in function of a contact detection mechanism, e.g., [15]. However, these robots had to approach the object slowly because of the above mentioned problems. One of the first applications of this kind of controllers to single link flexible robots was [16]. This controller was later extended to a two links — three degrees of freedom1 (DOF) flexible robot in [18], in which a hybrid position–force control combined with a collision detection algorithm was developed. These flexible robots could approach faster to the object. Contact detection mechanisms for flexible link robots were proposed that switched between controllers [19] or between references for a given controller [2]. The second controller was more robust than the first but less efficient. In [20], a contact detection mechanism was combined with a force control of two flexible fingers of a gripper of a 6 DOF manipulator in order to manipulate fragile objects. Finally, [21] described a hybrid position–force control of a sensing antenna that slides on a surface and recognizes an object by repetitive control. In all these works, rebounds may appear in the collision. Moreover, control robustness when contacting objects of unknown rigidity has not been addressed in most of them.

Previous methods switched controllers only once: the first time that the robot changed from free to constrained motion. If subsequent rebounds appeared, the control law was not varied (with the exception of [15] in which the contact detection mechanism remained ever active, switching controllers in the rebounds). Then robust asymptotic stability is required in the rebounds. Moreover, control should be robust to the unknown impedance of the collided object. In [22], the stability of a PD controller of a single link flexible robot that fed back the motor position in the case of rebounds with an unknown environment was proven, but force control was not achieved. Moreover, controlling motor position is not as efficient in removing vibrations of a flexible link as controlling tip position or the moment at certain points of the link.

We address the control of a single link flexible robot that has to exert a programmed force on an object. A fractional-order D tip position controller is combined with a feedforward position/force control. It cancels link vibrations better than [22] because it controls the tip position, which is clearly affected by link vibration, unlike the mentioned work that controls the motor position, which barely reflects link vibration. Moreover, the proposed control system attains higher stability robustness and phase margin than a PD tip position controller, which is the integer-order controller of complexity similar to the proposed one. Our control system also attains force control with nearly zero steady state error and is robust to nonlinear joint friction.

Fractional-order operators have been used to implement robust controllers. Applications to damping vibrations on flexible links are: a fractional-order proportional–derivativecontrol (FPD) of the attitude of a flexible spacecraft [23]; controls that include proportional and two fractional-order derivative terms of different orders for a planar two degrees of freedom flexible robot [24]; a FPD for a single link flexible robot robust to payload changes [25]; and a fractional-order proportional–integral controller for a flexible link implemented by an analog device denoted fractor [26].

Fractional-order hybrid position–force control of a rigid robot with compliant joints has been studied in [27]. Fractional-order controllers were also used in cooperation tasks between two manipulators with compliant joints in [28]. Our paper addresses for the first time the fractional-order force control of flexible link robots in contact tasks, that is robust to rebounds, environment uncertainties and joint friction.

Asymptotic stability in the case of rebounds is guaranteed by using a recent result on hybrid fractional-order systems developed in [29]. Robustness to joint friction is achieved by implementing a two nested loops control scheme. A relevant result of this paper is that, by using the proposed fractional-order D controller, higher phase margin, i.e. higher damping, than with a PD controller is guaranteed in all circumstances. Robust phase margin in contact tasks has not been proven in the previously mentioned controls neither others that can be found in the scientific literature. Flexible link robots are relatively fast systems that require efficient real-time implementations of their controls. Several software packages are available for analysis, design, simulation and implementation of fractional-order controllers (see [30]).

The remainder of this paper is organized as follows. Section 2 describes the dynamics of a single link flexible robot in the cases of free and constrained motion. Section 3 proposes our robust control scheme. Section 4 presents the experimental platform and some experimental results. Section 5 draws some concluding remarks.

Section snippets

System modeling

We address the control of a single link flexible robot moving in a horizontal plane. Owing to the mass distributed through the link, the dynamics of this robot is described by the Euler–Bernoulli partial differential equation (PDE) of a beam, e.g. [31], EI4w(x,t)x4+ρ2w(x,t)t2+υlw(x,t)t=f(x,t)where f(x,t) is a distributed external force and w(x,t) is the elastic deflection measured from the undeformed beam. Moreover, a flexible beam with uniform linear mass density ρ, uniform bending

Control system

This section develops a new fractional-order robust control system for single link flexible robots. It aims to control the tip position in the free motion case and the force exerted by the tip on the environment in the constrained motion case. In order to achieve this, the entire control problem is divided into three parts: (1) free motion control; (2) constrained motion control; and (3) contact detection algorithm.

A unique closed-loop controller is used all the time in order to provide with

Description of the platform

In this work, a slender antenna made of carbon fiber has been used as lightweight flexible link in order to verify the proposed control scheme. The link is attached to a DC mini servo actuator PMA-5A motor set (from harmonic drive) which includes a reduction gear n=100. The sensory system has an incremental optical encoder to measure the angular position of the motor, θm, and a sensor in the base of the link which measures the forces and the torques in the three abscissas (F–T sensor). This

Conclusions

This paper has investigated the force control of a single-link flexible manipulator. Control of flexible robots is of interest in several applications like assembly tasks and collision minimization when the robot works with humans.

A fractional-order controller combined with a collision detection mechanism has been designed and implemented in order to accomplish five main control objectives: (1) the manipulator must exert a programmed force on the environment, (2) it must be robustly stable to

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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    This work has been supported in part by the Spanish Agencia Estatal de Investigación (AEI) under Project DPI2016-80547-R (Ministerio de Economía y Competitividad), in part by the European Social Fund (FEDER, EU) and in part by the Spanish scholarship FPU14/02256 of the FPU Program of the Ministerio de Educación, Cultura y Deporte.

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