UCSD Robotic Skateboard

Objectives

The initial objective of the team was to show the basic scientific principle of conservation of energy through the creation of a robotic skateboard at a Science Outreach Event. In order to illustrate this principle, it was critical to understand what problem(s) was to be solved. For the purpose of the demonstration, dropping into a half-pipe was used an example for its similarity to a ball swinging on a pendulum. The ball loses energy as it swings from one side of its arc to the next due to friction, tension, and heat loss. During skateboarding, friction is the main culprit of loss of energy and for simplicity was taken as the main problem to be solved in the demonstration.For a skateboarder, the problem was solved simply through an act called "pumping". "Pumping" involves tucking in of the body as the skateboarder reaches the bottom of the arc of a half-pipe and extending the body as it reaches the top of the arc. This motion was similar to tucking in and extending ones legs as he swings on a swing set and increases the speed at which the one travels up the arc of the swing set. Through this motion, in skateboarding, friction was overcome in such a way that allows the energy to be conserved and the skateboarder to continue moving through the half-pipe. After the Science Outreach Event, the objective was changed to move forward and build upon the design that had been created. From that point, the team would move to allow the robot to actuate its masses with enough force in order to allow the skateboard to pump up the half pipe ramp and into the air. Furthermore, the robot would be designed in order to turn 180 degrees (or more) while in the air and above of the half-pipe.

Here is a video presenting a preliminary test of the pumping motion.

Process

One of the first steps in learning how to skateboard is pumping. Pumping is the action which allows the skateboarder to speed up within a half pipe or ramp in order to keep his momentum without touching the ground. Pumping adds energy to the skateboard to replace the energy lost by friction. The pumping action involves the skateboarder “pumping”, or extending, his legs upwards and lifting the upper body. In scientific terms, when the upper body lifts, the center of mass of the skater raises. This raising of the center of mass is what adds energy into the system.

The physics behind the addition of energy into a system can be modeled after a pendulum. The pendulum path represents a half-pipe and the mass at the end of the pendulum represents the center of mass of the skateboarder. When a skateboarder pumps, he raises his center of mass. In the pendulum model, the raising of mass is analogous to shortening the length of the pendulum. As the length of the pendulum is shortened, the pendulum must accelerate to conserve the angular momentum. This concept can be illustrated by Equation 1, where m is the mass of the pendulum, l the length, g the gravitational constant, θ is the position in radians, and ω is the angular acceleration. When the velocity increases, the energy of the system increases.

mlω² = mgsin(ϴ)       (1)

When the velocity increases, the energy of the system increases. This is a basic concept that can be seen in Equation 2, where v is the velocity of the mass.

 Kinetic Energy = (1/2)mv²     (2)

Another basic move that skateboarders do is a 180° spin. The skateboarder executes a multi-step process in order to complete the spin successfully. 

Step 1) The skateboarder prepares to spin his board, he pre-loads himself by turning his body opposite the spin motion. This is analogous to preloading a spring.

Step 2) He accelerates his upper body in the direction of the spin motion. The friction between the ground and the skateboard prevents the skateboarder’s lower body and the skateboard from  turning due to the reaction torque of the upper body accleration.

Step 3) As skateboard finally leaves the ground, the skateboarder locks his upper and lower bodies together. The momentum from the upper body carries the lower body into the spin. When the skateboarder locks his upper and lower body together, it can be modeled as an inelastic collision of his upper and lower body. For the robot, the principle that is demonstrated is the inelastic collision. During the collision, the velocity of the upper body dictates the speed of the combined masses. 

The following equation shows that the velocity of the top part of the body will travel as as a result of the final velocity of the spin, Vfinal, and the moments of inertias: It for the inertia of the arms, and Ib for the inertia of the body skateboard deck.

  Vtop = Vfinal*(It + Ib)/It 

            The robotic skateboard can perform two tricks. The robot performs pumping through arms which rotate from horizontal to vertical. The arms are weighted on one end and move in unison. When the arms move, they cause the robot’s center of mass to rise. Each arm is actuated by a position controlled gearmotor. The arm structure is attached to another gearmotor in the center of the robot which actuates the spin mechanism. The robot is controlled by an Arduino Uno microcontroller.

Design

The pumping mechanism of the robot sits upon the top of a cubic structure holds a “bulk head” which has all major components attached to it. The bulk head was machined out of aluminum square plates a 6.35 mm (¼ inch) thick of various lengths. The two major side plates have attachments in order to bolt and hold the arm lifting motors and gearboxes. A potentiometer was placed at the other end of the motor in order record the position of the arms. The bulk head also contains mechanical stops placed in specific positions in order to avoid the arms hitting the main cubic structure on the motion down, and themselves on motion upwards. The Motor Drivers were mounted and bolted on top of their respective motors.

The pumping apparatus on the robot consists of two foot-long arms which attach to DC-brush motors located on the center structure of the robot. The DC-motors are mated to 64:1 planetary gearboxes. The motors are powered by batteries located on the opposite end of the arms. The batteries act as the weight being lifted to raise the robot’s center of mass. The ingenious decision to use the batteries as weights lightens the robot by almost two kilograms. 

The spin mechanism is what actuates the 180 spin. The spin mechanism for the robot consists of a gearmotor supported by a thrust bearing. The motor shaft is mated to a block which couples the entire upper assembly to the lower assembly. When the motor spins, its shaft is stationary, but the entire motor and upper assembly rotates.

All electronics on the robot were placed in positions that would allow the robot to spin freely without fear of tangling. Therefore, all wires would meet at the top structure and the entire top structure would rotate.

Pumping Results

The robot was built and tested using our first and a newly constructed half pipe. During testing, it was found that the new flat section added friction and affected the timing necessary to pump in the half pipe. Therefore, the first half pipe was used to test because of our familiarity with the environment. 

Assumptions

-          Friction is the same while not pumping and while pumping

-          All energy lost is due to friction

-          All height gained is due to pumping

The following data was obtained from watching the skateboard in the halfpipe.

Table 1: Energy Lost Due to Friction

Table 2: Energy Gained in a Single Pump

Table 3: Maximum Energy Gained from Multiple Pumps

            From the results we see that pumping on the semicircle half pipe was the greatest success. Not only were we able to substation motion indefinitely, but also, we were able to gain significant height. In testing, we believe that we would be able to pump beyond the lip of the half pipe. However, we did not test it for fear of damaging the robot.

            Pumping on the half pipe with a flat section was a different story. From the results we can see that the flat section added almost twice as much friction into the system when compared to the semicircle half pipe. This added friction is large with respect to the amount of energy we could input in a single pump. In addition, timing the pumps properly in the flat section was more difficult because the flat section caused a pause between pumps. This pause made it more difficult to develop a rhythm and time pumps perfectly. In testing, we could only achieve five pumps because the timing was so difficult and the added friction. If we had more time to practice pumping, it may be possible to use the half pipe with the flat section.

            Regardless, both half pipes show an increase in height due to pumping. When using the semicircle half pipe, pumping is very obvious and apparent. The following video shows our results.

Spin Results

Using a pulley system, we were happy to discover that the robot could spin the way we wanted. At this point it was the first validation of our spin theory. Analyzing the video of the assisted spin, we found that the robot could complete a 180 in .3 seconds.

            Next, we tested the robot’s ability to do 180’s on a flat ground. We were surprised to find that on a low friction surface, the robot was able to do full 180’s almost 80% of the time. We tested the same robot parameters on concrete, and found that we could only spin about 90 degrees due to the increased friction.

At this point, knowing that our robot could accomplish 180’s on flat ground, we were confident that it was very likely that it could do a 180 on the half pipe because of the low friction and low gravity environment. Initially, we were reluctant to do any further testing for fear of damaging the robot. However, the thirst for knowledge and the importance of the scientific advancement of robotic skateboarding became too great. We decided to test the skateboard in the half pipe.

            On our very first test, we were amazed to see the robot completed a 150 degree turn! After three more tests, we were still stuck at about a 150 degree rotation. We decided to increase the spin motor’s voltage in order to increase the rotation.  Finally, after three more tries at this increased voltage, we successfully landed a 180 trick in front of all of our sponsors and a group of high school students from Preuss Highschool. Celebration, elation, and high-fives ensued. The following video shows some of our results.