Backends and dynamics

Native Rust

Classic Control integrates explicit ordinary differential or difference equations. Toy Text environments implement finite-state transition functions, with seeded randomness where transitions or card draws are stochastic.

Rapier2D

PhysicsWorld owns Rapier rigid bodies, colliders, joints, collision channels, and the query pipeline. Each step advances with an environment-selected \(\Delta t\). At a high level the constrained rigid-body system is

\[ M(q)\ddot q + C(q,\dot q) + g(q) = \tau + J(q)^T\lambda, \]

with joint/contact impulses \(\lambda\) resolved by Rapier. Environment pages specify the forces, motor controls, state projection, reward, and episode conditions layered over that solve.

MuJoCo

The optional mujoco feature exposes MjEnv, which loads XML, owns MuJoCo model/state objects, validates control length, and advances frame_skip internal steps. The agent timestep is

\[ \Delta t_{env} = \text{frame_skip},\Delta t_{model}. \]

MuJoCo solves multibody dynamics with actuation and constraints, conventionally written

\[ M(q)\dot v + c(q,v) = \tau(u) + J(q)^T f, \qquad q_{t+1}=\operatorname{integrate}(q_t,v_{t+1}). \]

MjEnv exposes qpos, qvel, controls, body kinematics, inertias, contact forces, tendon data, and actuator/constraint forces used to construct observations and rewards. Custom XML can change dimensions, ranges, timestep, and body names; environment-specific XML must retain every body/site name that its Rust implementation looks up.

References: Rapier rigid bodies, MuJoCo computation, and MuJoCo XML reference.