FORC · Lecture 8

Sampling-based predictive control and MPPI

Simeon Nedelchev

Candidate rollouts

Perturb a nominal control sequence.

Simulate each candidate with the same initial state.

Score the resulting trajectories.

w_i\propto\exp(-(S_i-S_{\min})/\lambda)

U\leftarrow U+\sum_i w_i\epsilon^{(i)}

Temperature controls weight concentration.

Costs: 2 and 4

Temperature: 1

Weights: 0.881 and 0.119

Perturbations $+1,-1$ give an update of about $+0.762$ .

The lab implements weighted stochastic shooting inspired by MPPI.

Formal MPPI needs additional assumptions and correction terms.

Clipping enforces input bounds.

Penalty costs alone do not guarantee collision avoidance.

MJX can batch compatible rollouts.

Sweep temperature, sample count, and noise scale.

Record effective sample size and missed control deadlines.

Reference: MuJoCo MJX