Autonomous Juggling Robot Paul Barsa Olivia Cao [email protected] [email protected] Shana Chen Krish Desai Aanya Gupta [email protected] [email protected] [email protected] Matthew VanDusen-Gross* Mary Pat Reiter* Ryan Wu* [email protected] [email protected] [email protected] New Jersey Governor’s School of Engineering and Technology July 27, 2019 *Corresponding Author Abstract—The art of juggling requires the brain to make two dimensions. This project seeks to use high speed linear decisions faster than human reaction time – a phenomenon that actuators in order to achieve the launch velocity required to has yet to be explained by modern science. By studying the drive marbles up the inclined plane into projectile motion. This juggling motion of a robot, it is possible to explore the methods through which the brain is able to translate a decision into an will be the first step to creating a robot that can use sensors action. The goal of this project was to create a robot that could to synthesize information and determine how to juggle on its accomplish two-dimensional juggling with up to five marbles in own. This robot can be studied to further understand the human a cascade, or with site-swap patterns. Computer-aided design brain and the human thought complex. was utilized to create models of linear actuators for the robot, and the Arduino platform was used to program the robot. The II. BACKGROUND robot was able to juggle one marble, perform a three ball cascade, and accomplish a three-one site-swap, albeit with inconsistencies. A. Logistics of Juggling A MatLab simulation was used to determine the paths that the marbles would have taken provided that the robot could Juggling has existed as a form of entertainment for over four accomplish juggling more balls and perform more complex site- thousand years, beginning in the Middle Kingdom in Egypt swaps. [5]. It was popularized in the 1920s by Enrico Rastelli, who, for nearly a century, held the record for juggling ten balls. I. INTRODUCTION The operations involved in juggling can be described In general, humans do not register the locations of individual through a series of mathematical algorithms rooted in physics balls while juggling. Instead, juggling is a dynamic, multi- and number theory. The mathematics of juggling rest on the dimensional task which combines instinct and reaction time, principle of an ideal environment, in which an object can be forcing humans to act within a feedback loop of information caught and then immediately thrown again [6]. This leads to [1]. Alex Barron, the world-record holder for juggling eleven the impossible implication that the object must achieve infinite balls, is able to track each ball that is thrown within 160 ms. acceleration in order to change direction instantaneously. The However, human reaction time is at best 200 ms for high fundamental tasks of “catching”, “carrying”, and “throwing” speed athletes, leaving many unanswered questions when it are reduced in theory to simply “catching” and “throwing” comes to how the human brain is able to control the body and [7]. In practice, humans are able to surmount this obstacle perform juggling [4]. Attempting to achieve this task with a by continuously adapting the launch velocity of the object. robot proves to be a significant challenge – while robots have For robots, this presents a much more serious issue; without the processing speed to match and surpass humans, they are human intuition, robots must rely on the laws of physics to limited in the necessary dexterity to perform such an operation, attempt to simulate the idealized situation. much less the instinctual feedback loop of information that Because of this complication, robots that use cameras and helps humans juggle [2]. computer vision would be able to juggle more efficiently, but The goal of this project is to create a sensorless robot given the extensive research done in the fields such as juggling that can juggle up to five balls in several different patterns, theory, it is possible to construct a sensorless robot that tracks transferring between them using an operation to generate balls only using the laws of physics. This project is similar to new sequences, known as a site-swap. This will be done on Shannons Machine, the first juggling robot created in 1970, an inclined plane which will reduce the acceleration due to as it is an open-loop system that depends upon physics rather gravity of the ball, and simplify the juggling pattern into than sensors. Another juggling robot, the Yale Planar Juggling 1 Robot created in 1989, was controlled by a mirror algorithm, a closed-loop system where the position and velocity of the pucks would be read in order to decide when to hit the pucks [3]. A robot that relies on sensor feedback is feasible, however, it is most achievable once a robot is created that can simply juggle balls without any sensor feedback. This approach has the added benefit of simplicity and cost efficacy, while still maintaining entertainment value. B. Spatial Awareness Humans have an innate spatial awareness that allow them to track the balls they are juggling without vision, and pre- dict where the balls will land in order to catch them. This project seeks to recreate the intrinsic property of the brain to predict an object’s trajectory and act accordingly. One theory that has been proposed to explain this phenomenon is the Fig. 1. Ladder diagram of five-three-one site-swap notation. “muscle memory” explanation. It claims that jugglers, after a certain amount of practice, have encoded responses to ball trajectories and hand movements in their brain so that they and R in the diagram represent the left and right hand of the move subconsciously. Another theory suggests that the brain juggler. The five-three-one pattern across the top of Figure 1 is able to determine the equations of motion rapidly to catch denotes that this ladder is representative of a five-three-one and throw the balls [4]. site-swap and guides the user in determining where to draw lines between the left and right hand. Above beat 1, there is a C. Site-swap Patterns 5. This means the first ball will be thrown in the air for 5 beats This project attempts to perform site-swap juggling which before being caught on beat 6 which is on the right-hand-side changes the beats at which the balls are thrown. To represent of the ladder. Above beat 2 is a 3. This means that the second this, Michael Day from the University of Cambridge, Paul ball will be thrown and caught within 3 beats ending in the Klimek from the University of California, Santa Cruz, and left hand. Above beat 3, there is a 1, meaning that the third Bruce Tiemann from the California Institute of Technology ball will be thrown and caught within 1 beat ending in the created site-swap notation in 1985 [9]. right hand. Then by following the colored arrow paths, the Site-swaps are denoted by the time intervals, or beats, viewer can visualize the pattern that the three balls follow in between throws. For instance, in a three-ball cascade (throwing a five-three-one site-swap. three balls in symmetrical arcs to the other hand), the first ball The ratio between the time the robot takes to catch and would be thrown on beats 1, 4, 7, etc.; the second ball would throw a ball and the time between catches is approximately 3:4 be thrown on beats 2, 5, 8, etc.; the third ball would be thrown [10]. This can aid in determining juggling patterns. However, on beats 3, 6, 9, etc. The site-swap notation for a three-ball as the number of balls increases, the ratio approaches 1:1. This cascade is denoted by a 3 since each ball is thrown after three suggests that there are limitations to the amount of balls that beats. can be juggled. In site-swaps, every ball has a respective ratio In this scenario, all of the balls were thrown within the and must be accounted for. same amount of beats each time. However, in a five-three-one site-swap, the ball thrown horizontally spends less time in the D. Open-Loop and Closed-Loop Strategies air compared to the balls thrown in the arcs. The first ball is One of the primary facets of human juggling is the feedback thrown and caught within five beats, the second ball is thrown loop that allows humans to not have to focus on all the balls and caught within three beats, and the third ball is thrown at the same time. Closed-Loop Systems are related to control and caught within one beat. The first ball would be thrown theory and reactive systems in that they take information from on beats 1, 6, 7, 12, etc. The second ball would be thrown on the end of the system and use that information to modify initial beats 2, 5, 8, 11, etc. The third ball would be thrown on beats parameters [11]. Many times, closed loop systems tend to use 3, 4, 9, 10, etc. computer vision software to determine inconsistencies within All site-swap notations can determine the amount of balls the trajectory of the ball [12] [13]. From that data, using needed to perform the trick by adding up all of the numbers inverse kinematics, the required corrections can be made to and averaging this value by the amount of numbers present. the launch vector [14] [15].