Lecture 2: Kinesthetic haptic devices: design, kinematics and dynamics

Transcription

1 ME 327: Design and Control of Haptic Systems Winter 2018 Lecture 2: Kinesthetic haptic devices: design, kinematics and dynamics Allison M. Okamura Stanford University

2 kinematics

3 transmission 2 Capstan drive Friction drive

4 x handle Hapkit kinematics r pulley pulley = r sector sector r handle x handle = r handle sector r sector sector r pulley pulley x handle = r handler pulley r sector pulley

5 position, velocity, and acceleration In this class, you will measure position and time data directly from your Hapkit position t 0 velocity 0 acceleration is usually too noisy time time v inst = dx dt =ẋ v avg = x t

6 Hapkit force/torque relationships F handle relationship between force and torque: = Fr r handle pulley r pulley = sector r sector F handle = sector r handle r sector sector r pulley pulley F handle = r sector r handle r pulley pulley

7 forward kinematics for higher degrees of freedom for mechanical trackers that use joint angle sensors, you need a map between joint space and Cartesian space fwd kinematics: from joint angles, calculate endpoint position

8 computing end-effector velocity forward kinematics tells us the endpoint position based on joint positions how do we calculate endpoint velocity from joint velocities? use a matrix called the Jacobian ẋ = J q

9 formulating the Jacobian multidimensional form of the chain rule: 1 q 2 q 2 + ẏ q 1 q 2 2 assemble in matrix form: apple ẋ ẏ @q 2 # apple q1 q 2 ẋ = J q

10 compute the necessary joint torques the Jacobian can also be used to relate joint torques to end-effector forces: = J T f this is a key equation for multi-degree-offreedom haptic devices

11 how do you get this equation? the Principle of virtual work f x = q f T x = T q states that changing the coordinate frame does not change the total work of a system f T J q = T f T J = T J T f = q

12 simplified dynamics

13 mass-damper model

14 free body diagram F b = bx, sum forces, equate to inertia: mx = F a F b mx + bx = F a

15 system block diagram x d human k h d dt x d b h k h b h f a + - f hand f total x h x h x h 1 m h b f dt dt T ( ) 1 2 device Computer J? cmd τ T J 1 f cmd Virtual Environment

16 rendering a wall (in one degree of freedom)

17 classic algorithm for rendering with an impedance-type device 1. read the position of the user from the haptic display 2. see if there is a collision with objects in the virtual environment 3. if there is, calculate forces 4. send corresponding torque commands to motors, and change the virtual environment state

18 static rigid body interaction the virtual environment pretends that the user is holding onto a fictional rigid body though the haptic device handle this rigid body interacts with other rigid bodies in the virtual environment. with impedance control, nothing is perfectly rigid: F = kx

19 rendering a simple wall

20 when the tool is not a point

21 discussion in what ways does this algorithm feel like a real wall? in what ways does it not? how could you make it feel more like a real wall?

22 visual feedback of stiffness Actual: trick: never show the point penetrating the surface, even if it is psychophysical studies have shown that this makes the Visual display: surface appear stiffer/harder

23 displaying impact vibrations Okamura, et al Kuchenbecker, et al. 2006

24 aside: wall realism evaluation Kuchenbecker, et al. 2006

25 kinesthetic device examples

26 K. Kuchenbecker

27 K. Kuchenbecker

28 K. Kuchenbecker

29 Types of Devices Florian Gosselin, CEA

30 Types of devices K. Kuchenbecker

31 kinesthetic device challenges competing goals of high stiffness and low mass force feedback feels soft - Nerf World point-based interactions are overly simple devices of sufficient quality are expensive limited workspace size, degrees of freedom, and actuation power usually constrained to sit at a desk no programmable tactile feedback

32 fill out the survey (return in class today if not done already) pay lab materials fee ($50 check made out to Stanford University, by class time Thursday 9/18) attend seminar tomorrow 12-1 pm, with Mark Cutkosky in (Jordan Hall) do Assignment #1 do your 3D printing as early as possible!

33 Assignment 1 due 1/18 1. Readings (no pts.) 2. Design and 3D print your Hapkit handle (10 pts.) Can start tomorrow 1/12 3. Haptics application ideas (10 pts.) 4. Haptic device simulation (30 pts.) We will notify you when the electronic submission folders on Box are ready

34 Office Hours Jake: Mondays am in Nathan: Wednesdays 3-5 pm in Allison: TBD (D'Arbeloff Teaching Lab) schedule is online You can also post questions to piazza You can also us for an appointment (please all three of us and be sure to state your available times for the next couple of days)

35 Haptics Demo with Phantom Omni/Geomagic Touch