I’ve been really slack about ironing out the last few bugs and taking some video of B.E.T.H. in action… But here it is! Some of the movements are a little erratic, but that’s because i’m filming with one hand while controlling the dual joystick controller with the other.

Here is a body forward kinematics demo. Here you can see that i can input body angles via the controller and the legs move as necessary to allow the body rotation without moving the feet.

Next is the tripod gait. This is a simple and fast gait in which two sets of three legs forming a triangle move alternately.

This is a wave gait. The wave gait is slow and moves only one foot at a time. The rest of the legs have to pull backwards in unison.

Finally, we have my favorite, the ripple gait. Two legs move at a time with one leg beginning to step as the other hits it’s peak height in the step. Because two legs move at once, its faster than the wave gait, but slower than the tripod.

For more info on gaits, here is a good article from Oricom Tech. My final code used here is available on my GitHub.

For more info on B.E.T.H., head back to the beginning.

A few weeks ago I got a Raspberry Pi to run in B.E.T.H. I had been running it all strewn around on the desk, but yesterday I finally got it all packed inside the chassis. Here’s a run down of what I did.

Parts:

• Raspberry Pi Model B with yellow composite video connector removed
• Adafruit Pi Proto Plate
• Sparkfun Xbee Breakout Board
• Trossen Voltage Regulator Breakout Board
• Murata OKI-78SR-5/1.5-W36H-C 5V Switching Regulator
• Dynamixel Hub
• Powered Dynamixel Hub
• USB2AX USB Dynamixel Adapter
• D-Link DWA-131 USB Wifi Adapter

So as you can see, I mounted the Xbee breakout on the Pi Proto Plate. At first the Plate was sitting up too tall. It originally was the full length of the Raspberry Pi and spaced up enough using an extended header that it covered the ethernet and USB ports. I ended up cutting the board down and mounting it on a standard height header so it could sit lower. I mounted the Pi by glue gunning it to plastic standoffs which screw into the chassis.

As for power, I’m running the battery power into the regulator breakout board and using it as a distribution block to jumper battery power to the power Dynamixel hub. The 5V output of the regulator goes to the Raspberry Pi. I’m powering the Pi through the GPIO power pins accessed through the Pi Proto Plate.

I plan to order shorter Dynamixel cables and shorten up the battery/switch wires to clean things up, but as of now it looks like this:

Unfortunately the battery has to go on top of the robot. I now run the wifi adapter and USB2AX in the Pi’s USB ports. I then SSH and/or VNC in over the network to work on bot. If i have to I can reach in and plug a USB hub cable in in place of the wifi adapter.

Back to B.E.T.H.’s main index.

In the previous post, I went over my initial linear approach to stepping and why it didn’t work out so well. This post outlines my current method which is working much better.

The new method uses a sinusoidal “arch” shaped step in the ZX plane. This also works out well since a single sine function can cover the raise and lower part of the step in one time segment. By using a sinusoidal function for the front-to-back stepping in the X direction as well, i could cut the number of case in half to just two. The final benefit is that it produces a very smooth and natural motion with the smooth curves and foot speeds. Here’s what step code looks like:

switch (caseStep[legNum]){

                case 1: //forward raise and lower

                    leg[legNum].footPos.x = -amplitudeX*cos(M_PI*tick/numTicks);
                    leg[legNum].footPos.y = -amplitudeY*cos(M_PI*tick/numTicks);
                    leg[legNum].footPos.z = -abs(amplitudeZ)*sin(M_PI*tick/numTicks);

                    if( tick >= numTicks-1 ) caseStep[legNum] = 2;
                    break;

                case 2: // pull back

                    leg[legNum].footPos.x = amplitudeX*cos(M_PI*tick/numTicks);
                    leg[legNum].footPos.y = amplitudeY*cos(M_PI*tick/numTicks);
                    leg[legNum].footPos.z = 0;

                    if( tick >= numTicks-1 ) caseStep[legNum] = 1;
                    break;

          }// end of case statement

As you noticed, the sequencing itself is carried out by the case statement block. They key to the sequencing is in the caseStep[] array. The array has six elements, one for each leg. The variable defines at which case each leg begins. For a tripod gait, the front right leg (#1), rear right (#3), and middle left (#5) leg all start at the first case and step together. The other legs start 180deg off which is the second case. So for my prior four-case linear “triangle” step function, caseStep[] is defined as {1,3,1,3,1,3}. For the new two-case “sine” step function, caseStep[] is defined as {1,2,1,2,1,2}.

Each case statement increments caseStep[] to the next case in order to advance to the next portion of the foot step. The final code looks like:

/*************************************************
  tripodGaitSine()

**************************************************/
void tripodGaitSine(){

    float sinRotZ, cosRotZ;
    int totalX, totalY;
    float rotSpeedOffsetX[6], rotSpeedOffsetY[6];
    float amplitudeX, amplitudeY, amplitudeZ;
    int duration;
    int numTicks;
    int speedX, speedY, speedR;

    if( (abs(commanderInput.Xspeed) > 5) || (abs(commanderInput.Yspeed) > 5) || (abs(commanderInput.Rspeed) > 5 ) ){

        duration = 500;                               //duration of one step cycle (ms)
        numTicks = round(duration / SERVO_UPDATE_PERIOD / 2.0); //total ticks divided into the two cases

        speedX = 180*commanderInput.Xspeed/127;        //180mm/s top speed for 180mmm stride in one sec
        speedY = 180*commanderInput.Yspeed/127;        //180mm/s top speed
        speedR = 40*commanderInput.Rspeed/127;         //40deg/s top rotation speed

        sinRotZ = sin(radians(speedR));
        cosRotZ = cos(radians(speedR));

        for( int legNum=0; legNum<6; legNum++){                        totalX = leg[legNum].initialFootPos.x + leg[legNum].legBasePos.x;              totalY = leg[legNum].initialFootPos.y + leg[legNum].legBasePos.y;                          rotSpeedOffsetX[legNum] = totalY*sinRotZ + totalX*cosRotZ - totalX;               rotSpeedOffsetY[legNum] = totalY*cosRotZ - totalX*sinRotZ - totalY;                           if( abs(speedX + rotSpeedOffsetX[legNum]) > abs(speedY + rotSpeedOffsetY[legNum]) )
		amplitudeZ = ((speedX + rotSpeedOffsetX[legNum])*duration/3000.0);
            else
		amplitudeZ = ((speedY + rotSpeedOffsetY[legNum])*duration/3000.0);

            amplitudeX = ((speedX + rotSpeedOffsetX[legNum])*duration/2000.0);
            amplitudeY = ((speedY + rotSpeedOffsetY[legNum])*duration/2000.0);

            switch (caseStep[legNum]){

                case 1: //forward raise and lower

                    leg[legNum].footPos.x = -amplitudeX*cos(M_PI*tick/numTicks);
                    leg[legNum].footPos.y = -amplitudeY*cos(M_PI*tick/numTicks);
                    leg[legNum].footPos.z = -abs(amplitudeZ)*sin(M_PI*tick/numTicks);

                    if( tick >= numTicks-1 ) caseStep[legNum] = 2;
                    break;

                case 2: // pull back

                    leg[legNum].footPos.x = amplitudeX*cos(M_PI*tick/numTicks);
                    leg[legNum].footPos.y = amplitudeY*cos(M_PI*tick/numTicks);
                    leg[legNum].footPos.z = 0;

                    if( tick >= numTicks-1 ) caseStep[legNum] = 1;
                    break;

          }// end of case statement

        }// end of loop over legs
        if (tick < numTicks-1) tick++;
        else tick = 0;

    }//end if joystick active

}

I think it needs a little fine tuning of the speeds and step durations, but its essentially done. B.E.T.H. is now fully mobile!

Check out where this all began.