Physics Simulators

synapsys.simulators provides nonlinear continuous-time physics simulators with a unified interface for control design, testing, and reinforcement learning.

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Available simulators

Class	System	States	Inputs	Outputs
MassSpringDamperSim	1-DOF linear MSD	[q, q̇]	[F]	[q]
InvertedPendulumSim	Nonlinear pendulum on fixed pivot	[θ, θ̇]	[τ]	[θ]
CartPoleSim	Lagrangian cart-pole	[p, ṗ, θ, θ̇]	[F]	[p, θ]

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Common interface

Every simulator inherits from SimulatorBase and exposes the same API:

from synapsys.simulators import CartPoleSim

sim = CartPoleSim()
y = sim.reset()                   # reset → initial observation
y, info = sim.step(u, dt=0.02)    # advance one step
ss  = sim.linearize(x0, u0)      # numerical linearisation → StateSpace

step() info dict

y, info = sim.step(u, dt=0.02)
info["x"]       # full state after step
info["t_step"]  # integration time (= dt)
info["failed"]  # True when the system left its safe region

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Integrators

All simulators support three numerical integration methods selectable at construction:

Method	Accuracy	Speed	Recommended use
"euler"	Low	Fastest	Very small dt (≤ 1 ms), RL inner loops
"rk4"	High	Fast	Default — good balance
"rk45"	Very high	Slower	Reference / validation

sim = CartPoleSim(integrator="rk4")   # default
sim = CartPoleSim(integrator="euler") # fastest

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Noise and disturbances

sim = InvertedPendulumSim(noise_std=0.01, disturbance_std=0.05)

• noise_std — Gaussian noise added to every observation (sensor noise model)
• disturbance_std — Gaussian noise injected into the control input (process noise)

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Thread-safe parameter updates

All simulators support live parameter changes from a separate thread:

sim.set_params(m=0.5)     # InvertedPendulumSim
sim.set_params(m_c=2.0)   # CartPoleSim

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Failure detection

y, info = sim.step(u, dt)
if info["failed"]:
    sim.reset()

Simulator	Failure condition
CartPoleSim	|p| > 4.8 m or |θ| > π/3 rad
InvertedPendulumSim	|θ| > π/2 rad
MassSpringDamperSim	never (always stable)

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Linearisation

Every simulator exposes linearize(x0, u0) which returns a continuous-time StateSpace via central finite differences — ready for LQR design:

from synapsys.algorithms.lqr import lqr

ss = sim.linearize(np.zeros(4), np.zeros(1))
K, _ = lqr(ss.A, ss.B, Q, R)