1. Neural Network Grasping Controller for Continuum Robots David Braganza, Darren M. Dawson, Ian D. Walker, and Nitendra Nath David 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? ●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 Robots Grasping Controller Design Neural Network Based Low Level Controller Evaluation of Tracking Performance with Neural Network Tracking Without Neural Network 1.03 x 10 6 1.04 x 10 6 17.71145.51 Controller with NN Controller without NN Performance measure Kinematic 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 Effector Control 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 VI continuum manipulator grasping a ball Improved performance is achieved by including the neural network in the low level joint controller Z t t 0 k q d ( ¿ ) ¡ q ( ¿ )k 2 d ¿ Z t t 0 k u ( ¿ )k 2 d ¿ is the robot Jacobian is the end effector position is the joint position U ( t ), J + n U e + ¡ I n ¡ J + n J n ¢ U m Tracking With Neural Network forces the end effector to encircle the object. U m ( t ) is a task space velocity field # ( x n ) is the task space position error e ( t ) U e, # ( x n ) + K e is a positive constant K is a null space controller which enables the body of the robot to avoid contact with the object. U m, ¡ k m £ J s ¡ I n ¡ J + n J n ¢¤ T y a is a repulsion function is a Jacobian like vector is a positive constant k m J s U e ( t ) The kinematic level controller is fused with the neural network controller using a filter which produces bounded trajectories q d ( s ), sa t ( U ) ¡ s ² + 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 = ^ W T ¹ ¾ ³ ^ V T x ´ is the input vector, and e 2, ( _ q d ¡ _ q ) + ( q d ¡ q ) x = h 1 q T d _ q T d Ä q T d ::: q d T i T Velocity Kinematics: Dynamic model: ^ W ; ^ V are adaptive weight estimates. M ( q ) Ä q + N ( q ; _ q ) + F e ( q ; _ q ) = ¿ M ( q ) N ( q ; _ q ) F e ( q ; _ q ) ¿ ( t ) q ( t ) _ x n = J n _ q J n ( q ) y a Red – Desired Trajectory, Blue – Actual Trajectory x n ( t ) J + n ( q ) ¿, ( K s + I n ) · e 2 ( t ) ¡ e 2 ( t 0 ) + Z t t 0 e 2 ( ¿ ) d ¿ ¸ + Z t t 0 h ¡ sgn ( e 2 ( ¿ )) + ^ f ( ¿ ) i d ¿ is the pseudo inverse of the robot Jacobian