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Acrobots is best used as an exploratory or enrichment tool as kids learn about forces and motion. Teachers could also use it to introduce these concepts during a physics unit. Have kids work in small groups to experiment with different settings. They should record the settings that they adjusted and make observations about how the acrobots change accordingly. Encourage kids to be as detailed as possible, noting the acrobots' connections, sizes, and movements. Follow up with a class discussion and make connections to real-world examples. Try to come up with challenges for your students: Who can build the highest tower? The longest chain? What settings help you construct different structures with the acrobots? Why?


Acrobots is a sandbox-style app that lets users manipulate multi-legged robots that wriggle, twist, and reach to connect with one another. At the start, a number of colorful acrobots appear on-screen. Icons for making changes are in the upper left corner of the screen: Tap a plus sign to add acrobots and a minus sign to remove them from the screen; tap the light bulb to change the acrobots from multicolored to all black.

By tapping the bull's-eye icon, kids can adjust eight settings (including size, gravity, balance, stickiness, atmosphere, speed, legs, and detail), and they can tap eight built-in settings combinations (with names like "teeter" and "zero-g"). Kids can then explore how those settings affect the acrobots as they tap, drag, and tilt their device to move, stack, and otherwise manipulate the acrobots on-screen. Kids can also shake their devices to randomly scatter the acrobots across the screen.

The idea behind this tool is intriguing, and gameplay is definitely absorbing: It's consistently engrossing to see what happens if you change the acrobots (add and remove legs! make them big or small!) and change their environment (see what happens with the gravity turned all the way down!).

However, the app's learning potential is limited without good guidance from text within the app or a teacher as a guide. It's neat that kids can adjust variables (like gravity and the number of legs the acrobots have), but there aren't descriptions of what these variables might mean in real life or what their ramifications are within the game. And while some settings are pretty self-explanatory, others are less so, and kids may be left wondering what "stickiness" and "detail" really mean. There's a great opportunity here to help kids explore physics concepts, but there's not much built into the app to help those observations transfer from the game to the real world. The in-game physics are definitely intriguing and engaging, but teachers will need to get creative on their own to connect gameplay to their classroom.

The movements of the acrobots are based on physics concepts, and kids can adjust the settings, experiment, and observe. Unfortunately, without instructions, context, or clear learning goals, this isn't a great standalone fit for learning.

The dynamics of acrobots, two-link underactuated system, have strong nonlinearity, so that gain scheduling (GS) control is suitable for stabilizing the system in a wide range of operation. In this paper, GS controller design problems for the attitude control are reduced to solving polynomially parameter-dependent linear matrix inequalities (PDLMIs). The polynomially PDLMIs are relaxed by matrix sum of squares (SOS) polynomials to find feasible solutions. Several reduction techniques are adopted to reduce the amount of computation for solving the SOS problems while direct formulations are too computationally expensive to solve. For two attitude modes of the acrobot, the effectiveness of GS control is shown by experiments as well as nonlinear simulations. 041b061a72


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