Research articleStable force control and contact transition of a single link flexible robot using a fractional-order 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 ), 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 ) 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: where is the speed of the robot, is the mass of the robot, is the mass of the impacted operator, and 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 and 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 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 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 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 () 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 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 controller, higher phase margin, i.e. higher damping, than with a 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], where is a distributed external force and is the elastic deflection measured from the undeformed beam. Moreover, a flexible beam with uniform linear mass density , 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 . The sensory system has an incremental optical encoder to measure the angular position of the motor, , 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.
References (40)
- et al.
Force control of a very lightweight single-link flexible arm based on coupling torque feedback
Mechatronics
(2009) - et al.
Collision detection and reaction for a multi-elastic-link robot arm
IFAC Proc Vol
(2014) - et al.
Fractional control: Fundamentals and user guide
Rev Iberoamericana Autom Inform Ind
(2016) - et al.
Strain gauge based control of single-link flexible very lightweight robots robust to payload changes
Mechatronics
(2005) - et al.
Vibration-free position control for a two degrees of freedom flexible-beam sensor
Mechatronics
(2015) - et al.
Motion control of a sensing antenna with a nonlinear input shaping technique
RIAI-Rev Iberoamericana Autom Inform Ind
(2016) Robot flexibles: Hacia una generación de robots con nuevas prestaciones
Rev Iberoamericana Autom Inform Ind
(2006)- et al.
Fast and soft arm tactics [robot arm design]
IEEE Robot Autom Mag
(2004) - Watson PC. Remote center compliance system, US Patent 4,098,001 (Jul. 4...
Historical perspective and state of the art in robot force control
Int J Robot Res
(1987)
Control of flexible manipulators: A survey
Robotica
Impedance control: an approach to manipulation: Part I, II & III
Trans ASME J Dyn Syst Meas Control
Hybrid position/force control of manipulators
J Dyn Syst Meas Control
Impedance control of a two degree-of-freedom planar flexible link manipulator using singular perturbation theory
Robotica
Modeling and quasi-static hybrid position/force control of constrained planar two-link flexible manipulators
IEEE Trans Robot Autom
Sensorless robot collision detection and hybrid force/motion control
Collision detection and safe reaction with the DLR-III lightweight manipulator arm
Force regulation and contact transition control
IEEE Control Syst
Force control of a single-link flexible robot based on a collision detection mechanism
IEE Proc Control Theory Appl
Cited by (35)
Force control of lightweight series elastic systems using enhanced disturbance observers
2023, Robotics and Autonomous SystemsA novel selected force controlling method for improving robotic grinding accuracy of complex curved blade
2022, ISA TransactionsCitation Excerpt :However, deep learning needs huge training data and its computing time is too long to delay control system cycle [22]. Although the algorithms and theories proposed by the above scholars could achieve high control accuracy in simulation model [23], it was difficult to achieve real-time response and real-time feedback due to the complex and changeable processing environment or the long processing time of these proposed algorithms [24,25]. However, above researches mainly focused on constant force control in whole surface profile of blade.
Design of multi innovation fractional LMS algorithm for parameter estimation of input nonlinear control autoregressive systems
2021, Applied Mathematical ModellingCitation Excerpt :The FC provides the possibility of computing real order integrals and derivatives [12,13]. The modelling and control procedures based on FC involve memory effects and provide a better insight to the system under study than the conventional approaches [14–17]. The superior performance of the fractional strategy is motivated the research community to develop FC based adaptive algorithms.
Robust stability of output feedback controlled fractional-order systems with structured uncertainties in all system coefficient matrices
2020, ISA TransactionsCitation Excerpt :This is mainly due to the global correlation and historical dependence of FOSs [8]. In addition, with the development of computer and artificial intelligence, fractional-order controllers have been explored in the application of various intelligent robots [9–13]. Stability analysis is a key issue in fractional-order control systems [14,15].
Model-free continuous nonsingular fast terminal sliding mode control for cable-driven manipulators
2020, ISA TransactionsCitation Excerpt :The major difficulties consist of much more complicated system dynamics, larger nonlinearities and joints flexibility. Many efforts have been made to achieve satisfactory performance for the systems with flexibilities [3–7]. Usually, relative precise dynamic model information is required to realize accurate trajectory tracking control, like adaptive control, inverse dynamic control, sliding mode (SM) control [8–15].
- ☆
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.