An energy-based formulation for soft-bodied virtual creatures, implemented in JavaScript + WebAssembly.
Instead of implementing simulations using explicit position update rules and manually derived force functions, we can implement simulations using gradient-based optimization on differentiable energy functions and compute forces and other derivatives using automatic differentiation. Automatic differentiation can be used for energy minimization and numerical integration.
This repository implements six energy functions: neo-Hookean triangles, controllable muscles, gravity, terrain collision, friction, and inertia (for backward Euler integration). The energy functions are implemented in C++ and differentiated with Enzyme. Additional functionality, including the optimization loop, is implemented in C++, compiled to WebAssembly, and wrapped as a JavaScript library.
You can create a simple simulation with one triangle and two muscles, where one muscle is controlled by a periodic signal, with the following HTML code.
<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
</head>
<body>
<script type="module">
import algovivo from "https://cdn.jsdelivr.net/gh/juniorrojas/algovivo@a03004d1f0b6dd2bbf92645800159b0fc71d817e/build/algovivo.min.mjs";
async function loadWasm() {
const response = await fetch("https://cdn.jsdelivr.net/gh/juniorrojas/algovivo@a03004d1f0b6dd2bbf92645800159b0fc71d817e/build/algovivo.wasm");
const wasm = await WebAssembly.instantiateStreaming(response);
return wasm.instance;
}
async function main() {
const system = new algovivo.System({
wasmInstance: await loadWasm()
});
system.set({
pos: [
[0, 0],
[2, 0],
[1, 1]
],
triangles: [
[0, 1, 2]
],
muscles: [
[0, 2],
[1, 2]
]
});
const viewport = new algovivo.SystemViewport({ system });
document.body.appendChild(viewport.domElement);
viewport.render();
let t = 0;
setInterval(() => {
system.a.set([
1,
0.2 + 0.8 * (Math.cos(t * 0.1) * 0.5 + 0.5)
]);
t++;
system.step();
viewport.render();
}, 1000 / 30);
}
main();
</script>
</body>
</html>The code above imports the ES6 module algovivo.min.mjs and loads the compiled WASM algovivo.wasm from jsDelivr. To serve these files from your own server, you can download them from the build branch.
Muscle commands can be specified with system.a.set([...]). A value of 1 means that the muscle is relaxed and wants to keep its original rest length. Values less than 1 indicate that the muscle wants to contract to some fraction of its original rest length.
system.a.set([0.3, 1]) |
system.a.set([1, 0.3]) |
system.a.set([0.3, 0.3]) |
|---|---|---|
 |
 |
 |
This is achieved using an action-dependent potential energy function for each muscle.
More details about this and other energy functions used in the simulation can be found here.
docker run -it -v $(pwd):/workspace juniorrojas/llvm-enzyme /bin/bash
export LLVM_BIN_DIR=/usr/lib/llvm-11/bin
export ENZYME=/Enzyme/enzyme/build/Enzyme/LLVMEnzyme-11.so
cd /workspace
./build.shnpm ci
npm run build