Reaching for redundant arms with human-like motion and compliance properties

https://doi.org/10.1016/j.robot.2014.07.012Get rights and content

Highlights

  • Novel controller for target reaching of redundant arms without trajectory planning.

  • The model-free control scheme guarantees desired completion time and accuracy.

  • Smooth natural reaching and configuration consistency in return motions.

  • Active compliance via admittance control for physical human–robot interaction.

  • Simulation and experimental results demonstrate human-like motion and compliance.

Abstract

This work proposes a redundant arm torque controller for reaching, guaranteeing desired completion time and accuracy requirements without the need for trajectory planning and prior knowledge of robot dynamics. The proposed controller is designed based on the prescribed performance control methodology and it is a reaching regulator in which the target pose for the hand acts as an attractor for the arm. It provides configuration consistency in return motions and hand and joint velocity smoothness. Its use in an admittance control scheme given measurements or estimates of external forces is also proposed providing active compliance capabilities in robot–environment interactions. Simulation studies for a 5dof human arm-like robot and experiments with a 7dof arm are performed to verify the approach and demonstrate the proposed controller’s performance.

Introduction

Reaching, a basic prerequisite task in service robotics, is related to the problem of addressing the ill-defined inverse kinematics of redundant manipulators yet far more demanding as it requires movements with human-like kinematic and compliance characteristics. Studies of human unconstrained reaching movements from one point to another reveal the following invariant kinematic characteristics: straight line paths, bell shaped velocities and joint configuration repeatability in repetitive motions  [1], [2], [3], [4]. Following the human-like paradigm, the proposed methods for realizing reaching, move away from the traditional two stage approach of path/trajectory planning and motion execution common to industrial robots, towards utilizing the reaching target as an attractor for the arm.

Task based pure kinematic controls are traditionally proposed and the solution of the ill-posed inverse kinematics is resolved either by introducing optimization of some performance criteria (e.g. manipulability, energy consumption, distance from a preferred posture, obstacle or joint limit avoidance)  [5], [6], or by exploiting the redundancy to execute lower priority tasks or reproduce human-like configurations like the elbow elevation angle  [7], [8]. Kinematic control laws however produce discontinuous joint velocity profiles in multi-task algorithms  [9]. They can furthermore get stuck to algorithmic singularities depending on target position  [10]. The stability of these methods is investigated under some simplifying assumptions in  [11], [12] leading to gain conditions.

On the other hand, proposed torque controllers include simple task based error regulation control laws utilizing the Jacobian transpose  [13], [14], [15], [16], [17], [18]. Based on the virtual spring-damper hypothesis and the introduction of appropriate joint damping factors  [13], [14], [15], attempts have been made to improve on the original work regarding bell-shaped velocity profiles, compliance to external forces and configuration consistency  [16], [17], [18] but are not supported by a stability analysis. Configuration repeatability is a human-like characteristic desirable in reaching motions as it enhances the legibility of the robot movement by humans. Repeatable generalized inverses or off-line planning were proposed to achieve repeatability  [19], [20] whereas controllers inspired by human muscle activation are reported to present repeatability characteristics  [18] but are not supported by a stability analysis.

Human likeness in terms of compliance to contact forces is an important issue related to both the physical human–robot interaction and the safety of the coexisting humans. Compliance can be achieved passively by using flexible components in the robot’s structure or actively by the control method; passive compliance is important for absorbing the impact energy while active compliance is instrumental for facilitating physical human–robot interaction  [21]. Collision detection and reaction strategies are similar to those developed for human intent detection and intent following control, during physical interaction. Early approaches for collision detection are based on measuring forces/torques, using full model dynamics and joint accelerations. Then, the residual torque method, based on the preservation of momentum, has reduced sensor needs, requiring only the use of the encoders available at the joints  [22]. Changes on the control effort signal of a gravity compensated system, were recently utilized to detect the physical contact  [23]. Reaction strategies extract the ‘intent’ or disturbance direction and magnitude and use it to achieve a safe reflex motion. In all cases, a switching strategy is adopted between the current robot task and the reaction law mainly by switching the commanded reference. However, switching may negatively affect stability of the overall switched system; achieving sufficient smoothness of the control signal under both modes of operation i.e., the unconstrained reaching task and the reaction under a contact force is important for stability and increased human safety potential.

This work focuses on what we consider fundamental in reaching performance to enhance robot acceptability in human–robot shared environments: accuracy in reaching a feasible target, time convergence imposed at will, smooth hand and joint velocity profiles, joint configuration consistency and active compliance to external forces to facilitate physical human–robot interaction. It is based on the prescribed performance control methodology (PPC) introduced in  [24]. PPC allows the designer to impose certain bounds on the output signals of nonlinear systems, and in some cases, without even using approximators to acquire information regarding the considered system dynamics  [25]. It has already been applied in controlling non-redundant robot motion and exerted force  [26], [27], [28], [29], [30] and was further used in a first attempt to resolve the unconstrained reaching task via a kinematic control law  [31]. A torque controller was then proposed in  [32] in a model based scheme utilizing the system dynamics as opposed to the controller presented here.

In this work we design a simple torque controller for redundant robotic arms which requires no prior knowledge of the robot model or its approximations neither a trajectory plan in order to reach a target as well as comply to an external force, if present. Unlike most of the multi-task kinematic algorithms, the proposed method produces continuous velocity profiles achieving target reaching within a pre-specified desired time and accuracy. Moreover, it avoids high initial accelerations producing smooth velocity profiles and consistent configurations as human muscle inspired schemes but unlike most of them is supported by a theoretical stability analysis. Simulations of a 5dof human arm-like robot and experiments with a KUKA LWR4 + 7dof arm validate and demonstrate controller performance in various scenarios.

Section snippets

Problem description

Consider a robot manipulator with n joints and a task space of dimension m with m<n, and let qn be the vector of the generalized joint variables. The dynamic model of the robot in free space motion is given by:H(q)q̈+C(q,q̇)q̇+G(q)=u where H(q)n×n is the positive definite robot inertia matrix, C(q,q̇)q̇n is the vector of the centripetal and Coriolis forces, G(q)n is the gravity force vector and un is the joint input vector. Let pm be the generalized position of the robot end

Prescribed performance control preliminaries for reaching tasks

The prescribed performance control methodology introduced in  [24] enables the design of controllers for a range of nonlinear system classes capable of guaranteeing a priori set performance bounds on the transient and steady state of the system output components ei(t) via the satisfaction of the following inequalities:Miρi(t)<ei(t)<ρi(t)tin caseei(0)0ρi(t)<ei(t)<Miρi(t)tin caseei(0)0 where ρi(t) called the prescribed performance function must be bounded, smooth and strictly positive and

Reaching control design

In order to enforce a desired reaching time and accuracy as well as induce a smooth bell shaped velocity characterizing human arm reaching motions a prescribed performance function ρi(t)(7) is associated with each task error coordinate ei with a constant Mi. Employing transformations εi=Ti(ei(t)ρi(t))(10), denoting by ϑTiTi(ei/ρi)1ρi>0 and ai(t)ρ̇i(t)ρi(t)>0,i=1,m, we propose the following intermediate control signal assuming that the arm stays away from singular positions:vqr=J(q)[a(t)e

Active compliance to external contact forces

It is clear that the proposed controller confines the task space error trajectory e(t) strictly within the prescribed performance boundaries dictated by the designer despite model uncertainties or external disturbances that may be caused by the dynamic interaction of the robot with its environment. However, compliance to external contact forces is required for successful physical human–robot collaboration. In that sense an admittance control scheme illustrated in Fig. 3 is proposed, realizing a

Simulation results

For simulations, a 5dof arm with geometry and parameter values corresponding to the average male adult, was borrowed from  [13]. It consisted of the upper arm with double axes of rotation, the shoulder joint, the forearm, the palm and the index finger. The last four axes allow motion on a plane while the first axis allows up and down movements. The arm’s length is 74.5 cm at full extension. Its kinematic and dynamic parameters are shown in Table 1. The prescribed performance parameters for the

Experimental results

The setup consists of a KUKA LWR4 + 7dof manipulator, the KUKA KRC2 controller and an external computer. The external computer is connected to the KRC2 via ethernet, utilizing a point-to-point dedicated network. The proposed controller is implemented in C++ utilizing the FRI library provided by KUKA. The control frequency is 500 Hz. KUKA, via the FRI position controller, allows a kinematic control implementation. The intermediate control signal vqr=J(q)[a(t)e+kpϑTεṗr] is implemented via

Conclusions

This work proposes a target reaching method for redundant robotic arms which utilizes a dynamic feedback law to generate and simultaneously control the motion in real time satisfying preset motion attributes without the need to design a trajectory in the task space. Although the controller does not rely on any knowledge regarding the robot dynamics or the utilization of robot model approximators, achieves smooth reaching movements characterized by straight line paths, bell-shaped velocity

Acknowledgments

This research is co-financed by the EU-ESF and Greek national funds through the operational program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)–Research Funding Program ARISTEIA I, Grant No. 506.

Abdelrahem Atawnih was born in 1978. He is currently a Ph.D. student in the Department of Electrical and Computer Engineering, of the Aristotle University of Thessaloniki, Greece. He received a B.Sc. degree in Electronics Engineering in 2002 from Al-Quds University, Palestine, and an M.Sc. degree in Electronics and Computer Engineering from the same University in 2005. His research interests are in the area of robot control.

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    Abdelrahem Atawnih was born in 1978. He is currently a Ph.D. student in the Department of Electrical and Computer Engineering, of the Aristotle University of Thessaloniki, Greece. He received a B.Sc. degree in Electronics Engineering in 2002 from Al-Quds University, Palestine, and an M.Sc. degree in Electronics and Computer Engineering from the same University in 2005. His research interests are in the area of robot control.

    Dimitrios Papageorgiou was born in 1985. He is currently a Ph.D. student in the Department of Electrical and Computer Engineering, of the Aristotle University of Thessaloniki, Greece. He received a diploma in Electrical and Computer Engineering in 2013 from Aristotle University of Thessaloniki and a B.Sc. degree in Automation Engineering from Alexander Technological Educational Institute of Thessaloniki in 2009. His research interests are in the area of Physical Human–Robot Interaction.

    Zoe Doulgeri is currently a Professor in Robotics and Control of Manufacturing Systems with the Department of Electrical and Computer Engineering of the Aristotle University of Thessaloniki, Greece. She received a diploma in Electrical Engineering in 1980 from the Aristotle University, an M.Sc. in Control Systems in 1982, an M.Sc. in Social and Economic Studies in 1983 and a Ph.D. in Mechanical Engineering in 1987 from Imperial College, London, UK. Since 2012 she serves as an editor in the Journal of Intelligent and Robotic Systems. Her current research interests include object grasping and manipulation by robot fingers, non-model based control of robotic systems with prescribed performance guarantees, control of flexible joint robots, human like reaching motion for redundant manipulators and physical human–robot interaction.

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