pockit

Pockit is a Python toolkit for continuous-time optimal control and trajectory optimization. Define dynamics, costs, and constraints with SymPy expressions; Pockit transcribes them with Radau or Lobatto collocation and supplies sparse derivatives to Ipopt or SciPy.

Install Pockit Solve the first problem Read the mathematical reference

Start with a working solve

Install the package with the Ipopt backend:

pip install "pockit-optimal-control[ipopt]"

The distribution name is pockit-optimal-control; the Python import remains pockit. The minimum-time double-integrator tutorial walks through a complete build, initial guess, solve, dense validation, and plot. If native Ipopt installation is unavailable, use the SciPy backend.

Goal	Go to
Install the recommended solver stack	Install with Ipopt
Build and verify a first model	Solve your first problem
Decide between Ipopt and SciPy	Optimizer selection
Define dynamics, bounds, and objectives	Problem setup
Connect phases through events	Multi-phase modeling
Diagnose an inaccurate transcription	Error checks and mesh refinement

One workflow across domains

Maintained examples use the same composable structure:

system, phase = build_problem()
guess = initial_guess(phase)
solution = solve_problem(system, guess)
figure = plot_solution(solution)

Each example page states the continuous-time model, units, boundary and path constraints, discretization, and independent numerical checks. Reported results are reconstructed on dense physical-time grids rather than accepted solely from collocation nodes.

Examples by discipline

The maintained suite contains 33 runnable examples covering 23 conservatively grouped application areas. The navigation consolidates them into 12 broader groups, while the table below preserves the 23-area scope. Each linked page includes the background, equations, units, constraints, assumptions, limitations, and numerical checks.

Discipline	Maintained examples	Main modeling idea
Mathematics and variational problems	Brachistochrone	Nonlinear mechanics checked against an analytical cycloid
Control theory and numerical benchmarks	Double integrator, LQR, hyper-sensitive problem	Free time, Riccati verification, bang-bang control, and boundary layers
Robotics	Robot arm, free-flying robot, humanoid OSC/WBC, humanoid retargeting, planar quadrotor, 6-DoF drone	Coupled motion, task hierarchy, contacts, and nonredundant attitude coordinates
Aerospace engineering and astrodynamics	Earth-to-Venus transfer, two-stage rocket, Mars powered descent	Orbital elements, staging events, and constrained landing guidance
Planetary science and small-body operations	Bennu soft landing	Rotating-frame proximity dynamics, surface approach, and low-thrust guidance
Astronomy and precision pointing	Flexible telescope slew	Input shaping and residual-mode suppression
Physical oceanography	Ocean inertial current	Coriolis dynamics and a controllability-Gramian forcing benchmark
Structural engineering	Structural vibration control	Active damping of a flexible mode
Chemistry and reaction engineering	Batch reactor, reaction selectivity	Operating-regime changes and competing reaction pathways
Transportation engineering	Electric-vehicle eco-driving	Road phases, speed limits, and energy-time trade-offs
Epidemiology and public health	SIR intervention	Nonlinear transmission dynamics and a health-care capacity limit
Biomedical engineering and neuroscience	Neural stimulation	Minimum-effort excitation of nonlinear membrane dynamics
Building science	HVAC demand management	Thermal storage, comfort bounds, and time-of-use prices
Energy systems and electric power	Battery arbitrage	Conversion efficiency, terminal inventory, and cycling cost
Pharmacology	PK infusion	Multi-phase loading, effect-site delay, and steady maintenance
Quantum physics	Two-level state transfer	Bloch-sphere control with an analytical fluence bound
Macroeconomics	Ramsey growth	Intertemporal consumption and investment allocation
Quantitative finance	Optimal trade execution	Inventory risk and temporary market impact
Water-resources engineering	Reservoir flood control	Storage routing and constrained downstream release
Agricultural water management	Irrigation scheduling	Root-zone balance, rainfall, drainage, and crop stress
Ecology and resource economics	Bioeconomic fishery	Renewable stock dynamics and sustainable harvest
Communications engineering	Wireless transmission	Deadline-constrained water-filling power allocation
Scientific machine learning	Neural ODE XOR	Continuous-depth training with an analytical classifier check

Representative verified results

Robotics: dynamically feasible centroidal retargeting with friction and center-of-pressure margins.

Water resources: optimized release under storage and downstream-flow limits, with cumulative balance checks.

Machine learning: a shared continuous-depth flow verified against an analytical XOR classifier.

Core modeling capabilities

• Radau and Lobatto direct collocation with polynomial state and control interpolation
• Single- and multi-phase systems with phase-local dynamics and shared static parameters
• Fixed or free phase times, endpoint conditions, path constraints, event equations, and integral terms
• Symbolic sparse first- and second-order derivatives with reusable compiled functions
• Ipopt for large sparse nonlinear programs and SciPy trust-constr for a pure-Python backend
• Continuous-time reconstruction, dense feasibility checks, and optional mesh updates when a first discretization is insufficient

Known singular-arc limitation

Pockit does not currently provide a reliable, validated workflow for true singular arcs. Solver convergence alone is not certification. Read Singular Arcs: Identification and Current Limitations before modeling a control-affine problem with a suspected singular interval.

Continue with installation, or open the first complete solve.