FLEXIBLE TRAJECTORY GENERATION TO EXTEND

HUMAN-ROBOT INTERACTION WITH DYNAMIC

ENVIRONMENT ADAPTATION

Xavier Giralt

Research Group On Intelligent Robotics and Systems, Technical University of Catalonia, 08028 Barcelona, Spain

Josep Amat

Institute of Robotics and Industrial Informatics, Technical University of Catalonia, 08028 Barcelona, Spain

Keywords: Human-Robot Interaction.

Abstract: In our daily life, we use many elements that help us by means of a higher protection level (thimble, door

stop) or by improving our dexterity (funnel, compasses). Both kinds of elements allow us to execute well

known tasks with less concentration, faster, and, above all, improving performance. Like the real tools

mentioned above, in the robotics field, virtual constraints enhance human-machine interaction. This work

presents a multi-parametric behaviour model for an agent that increases task safety, and enables higher

integration possibilities. The model presented here allows the perturbation of a programmed task, by

introducing virtual elastic and viscous forces. This work presents the behaviour model, a description of it’s

implementation and experimental results in human-robot interaction.

1 INTRODUCTION

Some robotic applications need to benefit from the

accuracy and precision of a robotic system, while

preserving a degree of human control. Some of such

application fields are assistive or surgical robotics.

The goal of a robotic assistant is to provide motion

commands that enhance precision, stability, safety

and skilfulness. Significant research of assistant

robotics systems is illustrated in Dario et al (1999),

as an assistant for colonoscopy. In assistive

robotics, due to the difficulties in modelling the

environment with enough definition or under

changing scenarios, it is necessary to aid the robotic

arm to adapt its movements to the real environment

or to the needs of the user.

These requirements have motivated the study and

development of behaviour models. The model must

allow software-generated force, velocity and

position signals applied to human operators through

the robotic system. A behaviour model can improve

human performance in robot-assisted manipulation

tasks, restricting movements into a region,

constraining velocities in a specific direction and/or

introducing virtual correction forces. The presented

multi-parametric behaviour model allows perturbing

on-line a predefined path, applying forbidden region

restrictions, and tuning model parameters (like

masses, viscosity, and stiffness).

There’s many procedures performed nowadays

by surgical robots, most of them are in the

orthopaedic field, using CAD/CAM surgical

systems, or teleoperated surgical robots for

laparoscopic interventions. Examples of successful

procedures performed with the Zeus system are

reported in Zhou et al (2006). This success has been

achieved as a result of the human enhancement that

robotic-assisted surgery systems offer.

Despite this success, there are several key

challenges that require to be solved in order to

achieve a complete development of surgical robotic

systems. Kanade (2004) carries out an analysis of

technological barriers. Introduced in Rosenberg

(1993), virtual fixtures are playing an important role

in the development of human-machine cooperative

interaction enhancement. Several groups have

integrated different implementations of virtual

fixtures in surgical robotic systems, as described in

211

Giralt X. and Amat J. (2008).

FLEXIBLE TRAJECTORY GENERATION TO EXTEND HUMAN-ROBOT INTERACTION WITH DYNAMIC ENVIRONMENT ADAPTATION.

In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - RA, pages 211-214

DOI: 10.5220/0001501102110214

 SciTePress

Bettini et al (2002). The work presented increases

human capabilities, integrating three categories of

restrictions: geometric, kinematic and dynamic. On

the other hand, by being a parametric representation,

different responses can be achieved with the same

model. Changing the virtual mass, length, elasticity

and viscosity... the behaviour can be tuned according

to specifications of a certain task.

2 FLEXIBLE TRAJECTORY

GENERATION

2.1 Task Oriented Trajectories

Many robots execute tasks by repeating a

programmed sequence of movements. These

sequences can be stored either with teaching by

demonstration techniques or by using the

corresponding robot programming language.

The work presented here aims to provide some

means of changing this trajectory during the

execution of the programmed task, through the

action of a human that perturbs the robot movement

by steering the end effector in the desired direction,

with a given force,

The developed method is based on the definition

of the robot path by means of two functions:

() ( , , )

txyz= and () ( , , )Bt xyz= . As the

Figure 1 shows, the segment defined by

P and

is considered the non-perturbed position of the end-

effector.

The programmed path can be modified if an

external force is applied on the robot, or the

presence of an obstacle is detected on its way. In

both cases, the trajectory is modified producing an

elastic movement away from the trajectory of the

end-effector. Considering the two trajectory

functions

()

t and ()Bt , the resulting behaviour can

be compared with a cable car, where the cabin is

modelled by a linear segment held from two extreme

points. The two links are springs with non linear

behaviour endowed with damping. In this way the

end-effector trajectory (the cabin) can be moved

away with respect to the theoretical trajectory (the

cable) by applying a perturbation force which is

perceived by the user itself.

Figure 1: End-effector trajectory and the resulting forces.

The perturbation of the position caused by an

external interaction produces a movement away

from the position of the segment

() ()Pt Pt− . The

representation for one such segment can be seen in

Figure 1.

The perception of the increasing effort enables us

to get better results to produce smooth movements

with a reasonable effort of the user. The distance

'PP

−

and

'PP

−

that can be produced in each

movement is the result of the following four set of

forces: Two vectors

r and

r equivalent to the

forces and torques measured on the force sensor. A

second component is an elasticity force

e and

e . A third element is an attraction force

and

t , towards the non perturbed trajectory. And a

forth factor corresponds to viscosity,

v , that

contributes to smoothing the trajectory when the

robot returns to its programmed trajectory after a

perturbation.

The forces that appear at each instant are shown

in Figure 1. The resultant of these two systems, of

four forces each, is what determines the segment

dynamics.

2.2 Behaviour Model for the

Human-Robot Interaction

The implementation of this model uses the motion

equation for a rigid body. Below, the structure of

this implementation is described, as well as several

equations and concepts needed. For a system of

particles

()

t extends to

()

() () ()

txtvt=

(1)

We define the sum of forces acting at this

particle at time

t as ()

t . Then, if the particle’s

mass is m , the change of

()

t is defined by

()

() () ()/

tvtFtm

(2)

Given these equations, a simulation starts with

initial conditions for

(0)X and uses a numerical

ICINCO 2008 - International Conference on Informatics in Control, Automation and Robotics

212

solver to trail the change of

over time. When

simulating a rigid body,

()

() () () () ()

t xtRtPtLt=

(3)

With ()Rt representing the orientation of the

body,

() ()Pt M vt=⋅ it’s linear momentum and

() () ()Lt It t

=⋅ it’s angular momentum. Where the

mass,

, of the solid is constant; and the inertia

tensor is computed as

() () ()

body

tRtIRt= , with

body

also constant. With this, (2) is now

()

() () ()* () () ()

tvt tRtFt t

ωτ

(4)

Where

()

t is the sum of forces applied to the

body, and

()t

is the sum of torques applied to it.

Arrived at this point, different behaviours can be

designed and implemented changing parameters like

the mass, and the inertia tensor. But what brings

further capabilities of this model is the insertion of

virtual forces and torques, so that

()

t and ()t

become the sum of the external actions and the

virtual ones. This virtual forces and torques are

designed to add different types of constraints like

impedance walls, viscosity of the medium, forbidden

regions or elastic correction forces.

The basis of the proposed model is defined as a

rigid body with two masses and a rigid link between

them. The virtual environment is a spring connection

element between each of the masses and a reference

point, as well as a viscosity of the medium.

Using this model, the reference point location,

damping, elasticity, mass and rigid link length are

parameters. Also, a constant virtual force can be

added to the system in either solid or world

reference. The equations of the virtual forces in the

solid reference frame are:

1()(1())

olid world world

ARtAxt

−

=∗ −

(5)

1()(() 1)()

viscous solid solid solid

tvt P c

=+×⋅−

(6)

1()(1()1)()

elastic solid solid

tA tP k=−⋅

(7)

1 () 1 () 1 () 1 ()

solid elastic viscous constant

t F tF tF t=+ +

(8)

1() 1 1() 1 ()

solid solid solid constant

tP F t tΓ=× +Γ

(9)

The analogous equations can be written for the

second mass. At this point, the external forces can be

included in the model, and the resulting forces and

torques in the world reference are

1 () () ( 1 () 2 () ())

world solid solid extern

FtRtFtFtFt=∗ + +

(10)

1 () () ( 1 () 2 () ())

world solid solid extern

tRt t t tΓ = ∗ Γ +Γ +Γ

(11)

The added value that this model of behaviour

provides is based on the fact that both virtual and

real interactions are defined with a natural, intuitive

and transparent approach.

From the dynamic behaviour point of view, the

parameters that have been tuned for a desired

response are the mass, distance between the spheres,

viscosity of the medium and elasticity of the virtual

links.

These parameters can be fixed for a desired

performance during the execution of a task, but their

values can also be tight to a parameter that evolves

during the execution of the task. This dynamic

adaptation can be model based and environment

based. In the first case, both viscosity and elasticity

parameters are function of the minimum distance to

an object.

3 EXPERIMENTAL SYSTEM

An experimental setup has been designed in order to

evaluate the different behaviours, shown in Figure 2.

The system developed includes a 6 degrees of

freedom robotic arm manufactured by Stäubli, a

motion controller by Adept, an ATI force and torque

sensor and a Dell personal computer.

Figure 2: Experimental system used for the evaluation of

the proposed behaviour.

The robotic arm is initially programmed to

perform task. The trajectory is specified by either

position and orientation, transformation matrices or

two trajectory paths as mentioned before.

Geometric, cinematic and dynamic restrictions of the

robotic arm are also considered when the trajectory

is programmed.

The motion controller is programmed with a low

level firmware that computes motion commands. A

hybrid position/force control loop is running with a

16 millisecond period time. Motion orders can be

sent in either Cartesian or Joint type, as well as in

either incremental or absolute modes. The motion

FLEXIBLE TRAJECTORY GENERATION TO EXTEND HUMAN-ROBOT INTERACTION WITH DYNAMIC

ENVIRONMENT ADAPTATION

213

controller runs a communication server under

TCP/IP protocol.

The force sensor measures forces and torques

applied at the tool sustained by the robot. An analog

to digital converter hardware and a calibration

routine are called by the personal computer. As a

result, two vectors are ready to be introduced to the

behaviour model: external forces and torques.

The personal computer runs the hybrid

force/position control loop linked to the motion

controller and the force/torque sensor. As described

in next section, a set of algorithms have been

developed to accomplish all computing

requirements.

The control loop accomplishes the main

functionality of the software developed for the

system. The sequence of routines called at each

cycle is:

• Capture position and orientation of the robot

• Capture voltages at the force sensor

• Compute forces and torques from voltages

• Subtract weight of the tool using its orientation

• Calculate new state according to the behaviour

• Send new state to the motion controller

4B4B4 RESULTS AND CONCLUSIONS

The model proposed, based on a double virtual mass

body, and elastic and viscous links has been tested

with some results shown in Figure 3. Different

experiments have been designed and tested. Simple

tasks like object pick and place, path following or

surface polishing are accomplished. During the

execution of the overall task, a perturbation is

introduced by means of external forces and torques.

The system reacts to the perturbations measured by

the force sensor, computing new positions according

to the described model, and sending the perturbed

positions to the motion controller. After the real

perturbation, the virtual forces described earlier act

as guidance of the endpoint, smoothly driving the

end effector back to the pre-programmed path.

In order to increase human capabilities, some

cooperative tasks include virtual constraints. The

proposed model integrates three categories of

restrictions: geometric, kinematic and dynamic. In

order to accomplish the geometric constraints, a

proximity library (Giralt and Hernansanz 2006) and

a surface navigation method (Hernansanz et al 2007)

have been developed and incorporated.

As it’s a parametric model, different responses

can be achieved with the same model. By changing

the values of the virtual mass, elasticity and

viscosity, the behaviour can be tuned according to

specifications of a certain task.

Figure 3: Experimental results. The left picture shows the

perturbation of a trajectory by means of external forces.

The two below the picture describe numerical values of

the reaction. First graph is the evolution of the external

force applied to the endpoint of the manipulator. The

graph in the middle shows the evolution of velocity of the

end effector. Last graph describes position response to

these force steps.

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