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 [DPRG] Motor control Message index sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: [DPRG] Motor control Next message: [DPRG] Motor control Subject: [DPRG] Motor control From: Kipton Moravec kip at kdream.com Date: Sat Jun 7 17:46:00 CDT 2003 ```At 02:15 PM 6/7/03, Dale Wheat wrote: >David, > >Thanks for the good information about motor control. Thanks also for >explaining it to me in agonizing detail last Tuesday. Although I'm chomping >at the bit to understand PID motor speed control algorithms (which will be >fun, because I barely know what an integral (The I in PID) is and until last >Tuesday had no clue what a derivative (The D in PID) was), I have to make >sure I completely understand what has been covered so far. > >As usual, I'd like to go over a few points in some more detail, mostly >concerning units of measure. Please correct me if my assumptions are >incorrect. > >The "arbitrary scale" of -100 to +100 in the first method expresses a value >of power applied to the motors. This is "open-loop power control" and does >not take into account variations in motors/gears/wheels, friction, voltage, >slopes, etc. Applying an equal amount of power to both wheels does not >guarantee driving in a straight line. That is correct. That is "open-loop" control. By getting feedback from a sensor, like wheel encoders, you know how much the wheel turns, or the distance traveled. That is "closed-loop" control. The PID algorithm generates an estimate necessary to spin the wheels dispite the differences in "motors/gears/wheels, friction, voltage, slopes, etc." >The next step involves dealing with the abstract quantites velocity and >rotation. Velocity is defined as distance over time. For our purposes, the >distance can be measured in shaft encoder counts (which hopefully can be >accurately translated into some more traditional linear measurement like >feet, inches, furlongs, parsecs, etc.), while the time is broken down into >the units between each measurement made. On SR04, for example, the time is >50ms, since measurements are taken 20 times a second. So (linear) velocity >is expressed as encoder counts over timer ticks. That is correct. >Rotation (or more accurately rotational velocity) is defined as angular >displacement over time. To use the equations presented, where rotation is >added or subtracted from the left and right velocities, respectively, the >units of measure would of course have to be the same, namely encoder counts >over timer ticks. If the wheelbase (the effective distance between the >wheels) is expressed in encoder counts, then the angular displacement can >also be expressed in radians, using one of the odometry equations, >specifically "theta = (right - left) / wheelbase". The rotational velocity >can then be expressed as the angular displacement (either in radians or >encoder counts) per timer tick. > >If the observer (me) is looking down on the robot from a height (and until I >build a flying/hovering robot, I will be), rotation to the left >(counter-clockwise) would be expressed as a positive angle and rotation to >the right (clockwise) would be a negative angle. Since turning to the left >necessitates slowing down the left motor, or speeding up the right motor (or >both), shouldn't the equations be: > >Left_motor = Velocity - Rotation >Right_motor = Velocity + Rotation > >instead of the other way around? It depends on how you define your coordinate system. In general I do not like to mix units, so velocity and rotation can not be added or subtracted >from each other. Always work in common units. If you are working with speed, then stay in encoder ticks/ sec, or radians/timer tick or whatever you want. But do not mix them up. As a general rule, a good working system is to stay in encoder ticks/timer tick. That makes most of the lowest level calculations dealing with simpler integers, and not as complex other units like feet/sec. If you need feet/sec you can convert only when you need it. >This next step seems like it will make things much simpler when traveling in >a straight line (I wish!) or turning in place, but what about describing an >arc? It seems to me that it would be easier or at least more accurate to >make a turn about a point other than the center of the robot, since the >measured distances would be larger and suffer less from round-off error in >odometry, or would these benefits be outweighed by the increased cumulative >navigational error? It occurs to me that there should be a simple way to >express this given the level of abstraction already in place. The exact >translation escapes me at the moment. Also, since all my robots seem bound >and determined to travel in arcs, anyway, I think it would be wise to "go >with your strengths" and find a way to let them do what they do best, and >still do what I want. To describe an Arc one wheel turns at so many encoder ticks/timer tick, and the other wheel runs at a different encoder ticks/timer tick. (Don't forget you have to take into consideration the different diameters of the wheels.) >Any thoughts would be appreciated. All you other nav-geeks feel free to >pitch in. The last couple of days' discussion on "dead reckoning" have also >been enlightening. I would probably have "canned" arcs that I could choose from if that is the way you want to go. Calculate the speed (encoder ticks / timer tick) for how many ticks for each wheel to make the arc you desire. >Thanks, > >Dale Wheat >http://dalewheat.com >(972) 486-1317 >(800) 330-1915, access code 00 There is another approach to the problem. That is to route plan for every tick. Prior to reading the encoder value, you calculate what it should be to be on the path you desire at the speed you want. You do this for each wheel, and the wheel tracks the given path. This is different then the way David does it. David's approach commands the wheels to go at a certain speed. The PID Controller gets the wheels to that speed and holds that until something changes. It is hard to predict the ramp-up and how fast it will reach the desired speed. This can cause errors when turning. The approach I described you would set the ramp up for each sample. It is a tighter control, (and hopefully if used correctly) would reduce the angular errors (for turning). It is a little more complicated as you have to have a route planner as well as the PID control to stay on the route. Kip >----- Original Message ----- >From: "David P. Anderson" >To: >Sent: Saturday, June 07, 2003 11:18 AM >Subject: [DPRG] Motor control > > > > > > Howdy > > > > As per our discussion of motor control from last week's > > RBNO, I thought I'd try to summarize the scribblings on > > the whiteboard and perhaps clarify a couple of points. > > >(omitted) > > > Left_motor = Velocity + Rotation > > Right_motor = Velocity - Rotation > > >(omitted) > > > > Next week, the PID Speed Controller... > > > > hope this helps! > > cheers, > > dpa > > > > _______________________________________________ > > DPRGlist mailing list > > DPRGlist at dprg.org > > http://nimon.ncc.com/mailman/listinfo/dprglist > > > > > >_______________________________________________ >DPRGlist mailing list >DPRGlist at dprg.org >http://nimon.ncc.com/mailman/listinfo/dprglist ``` Previous message: [DPRG] Motor control Next message: [DPRG] Motor control Message index sorted by: [ date ] [ thread ] [ subject ] [ author ] More information about the DPRG mailing list