Finite Differencing

RobotDynamics allows the Jacobians to be calculated using finite differencing via FiniteDiff.jl instead of forward-mode automatic differentiation via ForwardDiff.jl. ForwardDiff tends to be faster, and obviously provides more accurate derivatives, but finite differencing will always work, even through lookup tables, calling external code, or other functions that may be difficult to diff through using ForwardDiff.

To use finite differencing, set the diffmethod trait to RobotDynamics.FiniteDifference(). For example, if we want to use finite differencing for the cartpole we can use the following line of code:

RobotDynamics.diffmethod(::Cartpole) = RobotDynamics.FiniteDifference()

The interface is exactly the same:

model = Cartpole()
z = KnotPoint(rand(model)..., 0.1)
F = RobotDynamics.DynamicsJacobian(model)
jacobian!(F, model, z)

To acheive zero allocation with FiniteDiff.jl, we need to pass in a JacobianCache. We can define this directly from the model and pass it to the Jacobian function:

cache = FiniteDiff.JacobianCache(model)
discrete_jacobian!(RK4, F, model, z, cache)

The difference method, datatype, and other options can be modified via the JacobianCache constructor:

cache = FiniteDiff.JacobianCache(model, Val(:central), Float64)