Neural Network Grasping Controller for Continuum RobotsNeural Network Grasping Controller for Continuum RobotsDavid Braganza, Darren M. Dawson, Ian D. Walker, and Nitendra NathDavid Braganza, Darren M. Dawson, Ian D. Walker, and Nitendra Nath

Department of Electrical and Computer Engineering, Clemson University, Clemson, SC 29634-0915, E-mail: dbragan@ces.clemson.edu

is the positive definite Inertia matrix, represents the remaining dynamic terms, is the environment/contact forces and is the control input.

What is Whole Arm Grasping?What is Whole Arm Grasping?

● Parallel jaw grippers have limited flexibility when manipulating objects

Small number of contact points The range of object dimensions and shapes which can be

grasped is limited

● Whole arm grasping involves a continuum manipulator wrapping its body around the object to be grasped

Large number of contact points Improved payload capacity Better grasp stability Objects of different dimensions and shapes

can be grasped

Kinematic and Dynamic Models for Continuum RobotsKinematic and Dynamic Models for Continuum Robots

Grasping Controller DesignGrasping Controller Design

Neural Network Based Low Level ControllerNeural Network Based Low Level Controller

Evaluation of Tracking Performance with Neural NetworkEvaluation of Tracking Performance with Neural Network

Tracking Without Neural Network

1.03 x 1061.04 x 106

17.71145.51

Controller with NN

Controller without NN

Performance measure

Kinematic Level Path PlannerKinematic Level Path Planner

• The kinematic level controller

• The continuum robots dynamic model is highly nonlinear and uncertain • There are no contact force sensors available• The whole arm grasping controller is developed based on the following assumptions:

The object model (its dimensions and Cartesian position) is known The object is a rigid body

Object Model

End EffectorControl

Body Self Motion Control

Kinematic Level Path Planning

Dimensions and Cartesian Position

Low Level Controller

Trajectory Generator

Neural Network

Controller

• The low level controller does not require the structure of dynamic model to be known.

• Also, it does not require the contact forces to be measurable.

Various parallel jaw grippers

Octarm VIcontinuum manipulatorgrasping aball

• Improved performance is achieved by including the neural network in the low level joint controller

Z t

t0

kqd(¿) ¡ q(¿)k2d¿

Z t

t0

ku(¿)k2d¿

is the robot Jacobian

is the end effector position

is the joint position

U(t) , J +n Ue+¡I n ¡ J +n J n

¢Um

Tracking With Neural Network

forces the end effector to encircle the object.

Um (t)

is a task space velocity field#(xn)

is the task space position errore(t)

Ue , #(xn) +K e

is a positive constantK

is a null space controller which enables the body of the robot to avoid contact with the object.

Um , ¡ km£J s¡I n ¡ J +n J n

¢¤T ya

is a repulsion function

is a Jacobian like vector

is a positive constantkm

J s

Ue(t)

• The kinematic level controller is fused with the neural network controller using a filter which produces bounded trajectories

qd (s) ,sat (U)

¡s²+1

¢¡s·+1

¢3

Desired trajectory generator

• A continuous nonlinear integral feedback controller with a neural network feedforward component is utilized

are positive definite matrices,K s;¡ filtered tracking error

The two layer neural network with sigmoid activation function is: f = WT ¹¾³VT x

´

is the input vector, and

e2 , ( _qd ¡ _q) + (qd ¡ q)

x =h1 qTd _qTd ÄqTd

:::qdTi T

Velocity Kinematics:

Dynamic model:

W;V are adaptive weight estimates.

M (q)Äq+N(q; _q) +Fe(q; _q) = ¿

M (q) N (q; _q)Fe(q; _q) ¿(t)

q(t)

_xn = J n _q J n(q)

ya

Red – Desired Trajectory, Blue – Actual Trajectory

xn(t)

J +n (q)

¿ , (K s +I n)·e2(t) ¡ e2(t0) +

Z t

t0

e2(¿)d¿¸+Z t

t0

h¡ sgn(e2(¿)) + f (¿)

id¿

is the pseudo inverse of the robot Jacobian