MPC Drone Trajectory Planner

Reference Path

MPC Parameters

Prediction horizon N 16 steps

Rollout samples K 48

Obstacle avoidance weight 60

Reference speed 1.0×

Live Readouts

Tracking error

0.00 m

Plan cost J

0.0

Replans executed

How it works

The drone is a point-mass with double-integrator dynamics driven by a bounded acceleration command u (the thrust vector, gravity-compensated):

p_(t+1) = p_t + v_t·dt
v_(t+1) = v_t + u_t·dt,   |u_t| ≤ u_max

At every replanning step the controller does not solve one trajectory analytically — it samples K random control sequences U_k = (u_0,…,u_(N-1)) around the current best guess, rolls each one forward through the dynamics, and scores it with the MPC cost over the horizon:

J(U) = Σ_(t=0)^(N-1) [ w_track·‖p_t − p_ref(t)‖² + w_u·‖u_t‖² + obstacle penalty(p_t) ]

This is Model Predictive Path Integral control (MPPI), a real sampling-based MPC variant used on physical quadrotors and ground robots when the dynamics or cost are too nonlinear for a closed-form QP solve. Instead of picking the single best sample, it blends all of them with an exponential (softmax) weight that favors low-cost rollouts:

w_k = exp(−J_k / λ)
u*_t = Σ_k w_k·u_(k,t)  /  Σ_k w_k

Only the first control u*_0 of the blended plan is ever executed on the real (simulated) vehicle. The rest of the plan becomes the warm-start for the next replanning cycle — the horizon is shifted forward by one step and re-optimized from the new state, which is the "receding horizon" that gives MPC its name. The translucent trail ahead of the drone is this predicted horizon, redrawn every replan; the obstacle penalty term is what bends that horizon around the sphere before the drone itself gets there.

Prediction horizon N — how many steps ahead the controller plans; longer horizons anticipate the obstacle earlier but cost more to sample.
Rollout samples K — more samples approximate the optimal control distribution more accurately, at the cost of more rollouts per replan.
Obstacle avoidance weight — scales the penalty for entering the obstacle's safety margin, trading tracking accuracy for clearance.

Drone (actual path) Reference path Predicted MPC horizon Obstacle safety zone

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Model Predictive Control: Drone Trajectory Planner