Examples

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Abstract

Small problems that highlight APIs: STL, impulsive dynamics, and toy costs.

• Brachistochrone — Brachistochrone problem: finding the fastest descent path.
• Brachistochrone Batched — Batched brachistochrone — two ways to solve four problems at once.
• Chen Allgoewer — Chen–Allgöwer unstable OCP (OpenSCvx port).
• Flappy Bird — Flappy Bird-style 2D navigation with impulsive vertical flaps.
• Hypersensitive — Hypersensitive optimal control benchmark: minimize ½∫(x²+u²) over a long horizon.
• Impulsive — Impulsive control example with mixed continuous/impulsive inputs.
• Stl Integer Variable — Simple example using ox.stl.IntegerVariable to enforce discrete-valued states.
• Stl Or — Very simple example using the GMSR-based STL Or operator (ox.stl.Or).

Aircraft

Runnable scripts in this category.

• Dynamic Soaring — Minimum wind-gradient dynamic soaring of a glider (Zhao 2004).
• Supersonic Time To Climb — Minimum time-to-climb of a supersonic aircraft (Bryson's interceptor).

Animations

Animation-oriented variants of arm, drone, and obstacle demos.

• 7 Dof Arm — Cinematic offline render of the 7-DOF arm pick-and-place example.
• Dr Vp Polytope — Cinematic offline render of the drone-racing-with-polytope-viewplanning example.
• Franka Fr3v2 Pick Place — Cinematic offline render of the Franka FR3 v2 pick-and-place example.
• Logo — Cinematic offline render of the ACL-logo-tracing drone example.
• Obstacle Avoidance Vmap — Cinematic offline render of the vmap obstacle-avoidance example.
• Senss Hop Lidar Camera — Viser-rendered nadir camera mp4 for the SENSS hop (LiDAR FOV / footprint).

Arm

Manipulator motion, pick-and-place, viewpoint planning, and collisions.

• 3 Dof Arm — 3-link robotic arm with Product of Exponentials forward kinematics.
• 7 Dof Arm — 7-DOF redundant arm pick-and-place with Product of Exponentials FK.
• 7 Dof Arm Collision — 7-DOF redundant arm pick-and-place with Product of Exponentials FK.
• 7 Dof Arm Vp — 7-DOF redundant arm with viewcone (wrist camera) constraints.
• Franka Fr3v2 Pick Place — Franka FR3 v2 pick-and-place with Product of Exponentials FK.
• Franka Fr3v2 Viewplanning — Franka FR3 v2 view planning — wrist camera viewcone + PoE FK.
• Franka Fr3v2 Viewplanning Nodal — Franka FR3 v2 view planning with nodal viewcone constraints — PoE FK.

Car

Dubins models with obstacles and STL logic, plus the minimum-lap-time racing family.

• Dubins Car — Dubins car path planning with obstacle avoidance.
• Dubins Car Disjoint — Dubins car with disjoint waypoint visiting constraints.
• Dubins Car Obstacle Conditional — Dubins car path planning with conditional velocity constraint using Cond operator.
• Dubins Car Obstacle Stl — Dubins car path planning with conditional velocity constraint using Cond operator.
• Dubins Car Stl Or — Dubins car with Signal Temporal Logic (STL) constraints using stljax.
• Dubins Car Waypoint Stl — Dubins car path planning with STL waypoint inside a 2-norm ball.
• Race Car Hybrid — Race car minimum-lap-time optimization with F1 2026-style energy deployment.
• Race Car Ice — Race car minimum-lap-time optimization, pure-combustion ablation.
• Race Car Mpc — Race car receding-horizon MPC (OpenSCvx formulation).
• Race Car Multi Agent — Multi-agent race: K hybrid cars racing wheel-to-wheel via batched MPC.
• Race Car Multi Agent Mpcc — Multi-agent race where the field tracks a precomputed optimal lap.
• Race Car Multi Agent Mpcc Ice — Multi-agent tracking race, pure-combustion ablation of the MPCC example.
• Race Car Openscvx — Race car minimum-lap-time trajectory optimization (OpenSCvx formulation).

Double Integrator

Runnable scripts in this category.

• Double Integrator Static — 1D double integrator with box bounds and terminal goal (OpenSCvx port).
• Maze Rrt Scp — 2D maze navigation: JAX wavefront planner + SCP refinement.
• Moving Safe Zones — 2D double integrator with STL moving safe zones.
• Obstacle Avoidance Vmap — Double integrator obstacle avoidance with Vmap for parallel constraint evaluation.
• Obstacle Avoidance Vmap 2d — Planar double integrator obstacle avoidance with Vmap for parallel constraints.

Drone

Racing, obstacle avoidance, viewpoint constraints, and related utilities.

• Boresight Trace Mpcc — MPCC SVG tracing: a quadrotor draws an SVG path with its camera boresight.
• Cinema Vp — Cinematic viewpoint planning for aerial filming.
• Cinema Vp Nodal — Cinematic viewpoint planning for aerial filming with nodal constraints.
• Dr Vp — Drone racing with continuous viewpoint constraints.
• Dr Vp Nodal — Drone racing with nodal viewpoint constraints.
• Dr Vp Polytope — Drone racing with continuous viewpoint constraints using polytope target arrangement.
• Drone Racing — 6-DOF quadrotor racing through sequential gates.
• Drone Racing Batched Gates — Batched quadrotor gate racing: solve over B perturbed gate layouts.
• Logo — 6-DOF quadrotor tracing out the Autonomous Controls Laboratory Logo
• Lunar Terrain Agl — 6DoF quadrotor A→B over SENNS lunar DEM at ~20 m AGL.
• Maze Scp — 6-DOF quadrotor maze navigation: JAX wavefront guess + SCP refinement.
• Moving Safe Columns — 6DoF quadrotor with STL moving safe columns.
• Obstacle Avoidance — 6-DOF quadrotor obstacle avoidance with ellipsoidal obstacles.
• Obstacle Avoidance Nodal — 6-DOF quadrotor obstacle avoidance with nodal constraints.
• Openscvx Logo — 6-DOF quadrotor tracing out the OpenSCvx logo
• Quadrotor Hector — Simple quadrotor dynamics example (OpenSCvx port).
• Quadrotor Zigzag — RobotZoo quadrotor zigzag waypoint tracking (OpenSCvx port).

Frax

Runnable scripts in this category.

• Panda Frax — Franka Panda joint-space point-to-point motion using frax dynamics.
• Panda Frax Pick Place — Franka Panda pick-and-place via frax rigid-body dynamics.
• Panda Frax Viewplanning — Franka Panda view planning — wrist camera viewcone via frax rigid-body dynamics.
• Panda Frax Waypoint — Franka Panda point-to-point motion with an intermediate EE waypoint (frax dynamics).
• Ur5e Pen Trace — UR5e pen tracing — drawing on a work surface with a tool-mounted pen via frax.
• Ur5e Pen Trace Mpcc — MPCC UR5e pen tracing: receding-horizon contouring control of a drawing arm.

MJX

MuJoCo MJX dynamics: cartpole, multi-body, and skydio-style models.

• Cartpole Mjx — Cartpole swing-up using MuJoCo MJX dynamics.
• Double Cartpole Mjx — Double-link cartpole swing-up using MuJoCo MJX dynamics.
• Skydio X2 Mjx — Skydio X2 quadrotor racing through sequential gates with MuJoCo MJX dynamics.
• Triple Cartpole 3d Mjx — 3D triple-link cartpole swing-up using MuJoCo MJX dynamics.
• Triple Cartpole Game — Triple-cartpole balancing game.
• Triple Cartpole Mjx — Triple-link cartpole swing-up using MuJoCo MJX dynamics.

MPC

Discrete-time MPC-style and realtime-style double integrator setups.

• Double Integrator Discrete — MPCC example: 3D double integrator tracking a circular reference trajectory (discrete).
• Double Integrator Drone Racing — MPCC drone racing: 3D double integrator with time-optimal reference trajectory.
• Dubins Car Circle Analytical — MPCC example: Dubins car tracking a circular reference trajectory.
• Dubins Car Circle Discrete — MPCC example: Dubins car tracking a circular reference trajectory (discrete).
• Realtime Double Integrator Drone Racing — Realtime MPCC drone racing: 3D double integrator with live visualization.

Multi Agent

Runnable scripts in this category.

• Ilqgames Three Agent — Three-agent heterogeneous navigation (OpenSCvx port of lqrax iLQGames).
• Ilqgames Three Agent Lqr — Three-agent iLQGames with original lqrax soft collision cost.
• Multi Agent Circle Swap — Multi-agent planar double integrator: circle swap with collision avoidance.

Pendulum

Runnable scripts in this category.

• Pendulum Swingup Ocp — Cart-pendulum single-shot swing-up OCP (OpenSCvx port).

Realtime

Receding-horizon and streaming demos built on shared base problems.

• 3DoF Pdg Realtime — Interactive real-time visualization for 3-DOF powered descent guidance.
• 6DoF Pdg Realtime — Interactive real-time visualization for 6-DoF powered descent guidance.
• 3DoF Pdg Realtime Base — 3-DOF Powered Descent Guidance (PDG) for planetary landing.
• 6DoF Pdg Realtime Base — 6-DoF powered descent guidance base problem for realtime OpenSCvx demos.
• Cinema Vp Realtime Base — Base problem setup for real-time cinematic viewpoint planning.
• Drone Racing Realtime Base — 6-DOF quadrotor racing through sequential gates.
• Dubins Car Realtime Base — Dubins car path planning with obstacle avoidance.
• Obstacle Avoidance Realtime Base — Base problem setup for real-time 6-DOF obstacle avoidance.
• Cinema Vp Realtime — Interactive real-time visualization for cinematic viewpoint planning using Viser.
• Drone Racing Realtime — Interactive real-time visualization for drone racing using Viser.
• Dubins Car Realtime — Interactive real-time visualization for Dubins car path planning using Viser.
• Obstacle Avoidance Realtime — Interactive real-time visualization for drone obstacle avoidance using Viser.

Rocket

Powered descent guidance sketches in 3-DOF and 6-DOF.

• 3DoF Pdg — 3-DOF Powered Descent Guidance (PDG) for planetary landing.
• 6DoF Pdg — 6DoF PDG Rocket Trajectory Optimization
• 6DoF Pdg Batched Ic — Batched 6-DoF powered descent guidance — solve_batched over initial conditions.
• 6DoF Pdg Stc — 6-DoF Powered Descent Guidance with true Compound State-Triggered Constraints (cSTC)
• 6DoF Pdg Stc Ifthen — 6-DoF Powered Descent Guidance with compound STCs via ox.stl.IfThen
• Ascent Launch Vehicle — 4-phase Delta II-style ascent from KSC (28.5° lat) to GTO, based on the benchmark from Betts,
• Reusable Launch Vehicle — Runnable script; full source on the detail page.
• Rocket Ilqr — 2D rocket landing OCP (OpenSCvx port of lqrax ilqr_example.ipynb).
• 6DoF Pdg Dem — 6DoF PDG on DEM terrain – realtime with viser.
• 6DoF Pdg Dem Static — 6DoF PDG – single static solve with DEM terrain landing.
• 6DoF Pdg Stc Senss — 6-DoF Powered Descent Guidance with true Compound State-Triggered Constraints (cSTC)
• 6DoF Pdg Stc Senss Gimbal — 6-DoF Powered Descent Guidance with true Compound State-Triggered Constraints (cSTC)
• 6DoF Pdg Stc Senss Gimbal Hop — 6-DoF cSTC hop: ascent from launch pad → apex waypoint → nearby land pad.
• 6DoF Pdg Stc Senss Hop — 6-DoF cSTC hop: ascent from launch pad → apex waypoint → nearby land pad.
• 6DoF Pdg Stc Senss Planar — 6-DoF Powered Descent Guidance with true Compound State-Triggered Constraints (cSTC)

Spacecraft

Orbital transfers, halo orbits, and relative-motion prox-ops style problems.

• Dual Deputy Inspection Cw — Dual-deputy relative-orbit inspection with CW dynamics.
• Halo Orbit — Southern L2 Halo orbit initial conditions definition
• Hohmann Transfer — Hohmann transfer with impulsive delta-v controls (LEO → GEO).
• Let Transfer — Low-Energy Transfer (LET) setup in Sun-Earth CR3BP with one departure impulse.
• Low Thrust Transfer — Low-Thrust Orbit Transfer using Modified Equinoctial Elements.
• Proxops Cw — Proximity Operations (ProxOps) using Clohessy-Wiltshire dynamics.
• Relative Loitering — Relative loitering in Earth-Moon CR3BP with CTCS box-violation regularization.

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Paths mirror the repo layout: examples/<category>/.... Utility modules (for example plotting helpers) are omitted from this index.