Dipartimento di Elettronica Informazione e Bioingegneria Robotics

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Sherilyn Garrison
6 years ago
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1 Dipartimento di Elettronica Informazione e Bioingegneria Robotics properties and performance 25

2 Redundancy first definition McKerrow When a manipulator can reach a specified position with more than one configuration of the linkages, the manipulator is said to be redundant. According to this definition, redundancy = more than one solution to the inverse kinematic transform As a consequence, all the robots in practice are redundant!

3 Consider the space n axes of motion m (max 6) dimension of space achievable by the hand r dimensions of the task space : n = m standard robot. a : n > m; when there is a reduction of m in specific configurations, the robot is in a degenerate configuration 2 : n > m; the robot is redundant. The configuration of the robot can change without changing the end-effector configuration. : m >r; when r is completely within the end-effector space, task redundancy. 4 : in any of those situations there can be examples where for a particular configuration there exists multiple solutions.

4 Redundancy new definitions : If the number of solutions to the IK is not unique but finite, the manipulator is said to have multiple solutions. PUMA, etc 2 : If the dimension of the joint space is greater than the dimension of end - effector space then the device is kinematically redundant. Barret arm, : If the task space is completely contained by, and has a lower dimensionality than the end effector space, the manipulator is said to be task redundant. Use a 6 dof arm to pick-up object from top

5 degenerations Sometimes a robot can have infinite solutions only for some cartesian points singular point or degeneration point degeneracy is a situation in which there are an infinite number of configurations of the manipulator that achieve the desired end-effector configuration. in such a configuration, one or more degrees of end-effector freedom is lost Planar RR for θ2 = ± π and l=l2 the origin is a degeneration point

6 degeneration of PUMA wrist - This robot is the PUMA wrist if the origins of the systems are in the same point. has the rotation axes, each ortogonal to the next. We build the hand matrix and see why it has degeneration 2 rotation axes may aligne

7 degeneration of PUMA wrist - 2 If θ2= θ α a d θ 9 d 2 θ2-9 θ d = = d C S S C C S S C d C S S C 2 2, A A A T ),, ( ),, ( Θ Ψ Φ = + = R T z y x p p p Trans d d C C S S S S C C = Θ Φ= + = = = d d p p p z y x + Φ Φ Φ Φ = d d C S S C T ) k ( ) tan( ) tan( π θ θ θ θ + + Φ= + Φ =

8 Precision measures Accuracy The degree to which actual position corresponds to desired or commanded position. Accuracy of a robot is determined by elements : the resolution of the control system, the mechanical inaccuracies ( linkages and gears) and deflections under different load conditions, and the minimum error that must be tolerated to operate the arm under closed servoloop operation. Absolute Accuracy The difference in position between a point called for by a robot's control system and the point actually achieved by the robot. The error is computed in Cartesian space. Important in robot programmed in Cartesian Space.

9 Repeatability The ability of a robot to reposition itself at a spot to which it is sent. It is a tolerance about a position. It is affected by resolution, hysteresis, and mechanical inaccuracies. It describes the positional error of the endeffector when it automatically returns to a previously designated point. It is a statistic measure. Resolution (spatial) specifies the smallest increment of motion by which the system can divide the work envelope. This is either a function of the smallest increment in position that the controller can command or the smallest incremental change in position that the controller can distinguish.

10 Resolution, repeatibility, accuracy In 2D - the target is teached (joint variables) or computed from Cartesian space Repeatability is higher than accuracy REPEATABILITY here reached points teached target point spatial resolution grid ACCURACY position error computed target point

11 Repeatibility vs accuracy High repeatability and accuracy low accuracy high repeatability high accuracy low repeatability

12 Accuracy depends on: Ambient (temperature, humidity, ); Kinematic parameters (D-H) Prototype different from product Need to calibrate the robot model (signature) Dynamic parameters (compliance, friction, ); Measuring problems (encoders o resolvers ); Numerical problems (loss of precision ); application (installation).

13 payload Payload The maximum total mass or weight that can be applied to the end of the robot arm without sacrifice of any of the applicable published specifications of the robot. Also referred to as Load Capacity. All the load to be attached to the wrist (including the hand) is payload Usually a few Kg in industrial robots

14 Cycle time Time to complete this pick and place cycle Usually less than sec inch O 2 inches O

15 Trends in industrial robots Versatility (redundant) remote control and web programmable Open controller Safety: compliant, soft, High payload

16 PA Mitsubishi 7 dof Open controller

17 PA

18 PUMA vs PA- dof weight payload repeatability Control box motors controller PUMA 5 or 6 kg 2 to 4 kg. mm 7.5x444.5x5mm DC proprietary PA- 7 5 kg kg. mm 46x225x95 mm AC open

19 WAM arm Barrett Technologies, MA Open controller in C 4 o 7 dof weight: 25 Kg Payload: 4 kg repeatability: 5 μm

20 KUKA LWR LIGHTWEIGHT ROBOT (LWR) The outer structure is made of aluminum. It has a payload capacity of 7 kg. Due to its low weight of just 6 kg, the robot is energyefficient and portable and can perform a wide range of different tasks.

21 Baxter Rethink Robotics (Boston) 4 dof $25, Food processing Transportation Plastic Metal Consumer goods

22 i-limb (UK) Hand prosthesys 2 dof each finger Thumb manually moved to alignement or opposition

23 HAL (Cyberdyne, Japan) wearable robot Height-,6mm Weight: Full Body Type approx. 2kg (Lower body approx. 5kg) Power - Battery Drive Charged battery( ACV) Continuous operating time 2.5 hours Motions- standing up from a chair, walking, climbing up and down stairs) Hold and lift heavy objects and more... - now in clinical trials

24 uses electromygram (EMG) sensors on the shoulders, hips, knees and elbows. using these signals, the machine can aid a human in walking, climbing stairs, and heavy lifting, and is designed to help the disabled. it helped a paralyzed man get within 5 yards of the summit of Breithorn Mountain in Switzerland. It s currently only available in Japan, but when it becomes available in the U.S. will e about $, a month to rent, or about to $6, to buy.

Inverse Kinematics. Given a desired position (p) & orientation (R) of the end-effector

Inverse Kinematics. Given a desired position (p) & orientation (R) of the end-effector Inverse Kinematics Given a desired position (p) & orientation (R) of the end-effector q ( q, q, q ) 1 2 n Find the joint variables which can bring the robot the desired configuration z y x 1 The Inverse