Minilink

Write the equations once. Simulate, analyze, control, plan, optimize, learn.

The user guide is the tutorial notebooks; this site is the API reference.

• README

• Showcase notebook

• Tutorial series 00–11

• Teaching notebooks

API reference

• Core
  • System
  • DynamicSystem
  • StepSystem
  • DiagramSystem
  • StepDiagramSystem
  • check_diagram_params()
  • add_systems()
  • series()
  • feedback()
  • closed_loop()
  • autowire()
  • resolve_standard_feedback()
  • StandardFeedbackWiring
  • default_computer_boundary_ports()
  • SampledSignals
  • Trajectory
  • interpolate_schedule()
  • Set
  • InputSet
  • BoxSet
  • BoxInputSet
  • SingletonSet
  • BallSet
  • CallableSet
  • IntersectionSet
  • is_finite_box()
  • CostFunction
  • QuadraticCost
  • TimeCost
  • SumCost
  • ScaledCost
  • RESERVED_IDS
  • BlockRoles
  • block_roles()
  • command_port()
  • require_command()
  • Roles
  • roles()
  • check_reserved_id()
  • plot_space_of()
  • ErrorDriven
  • Distribution
  • Gaussian
  • Uniform
  • Particles
  • Sampler
  • Shape
  • Sphere
  • Box
  • Union
  • Inflated
• Compile
  • validate_equation_shapes()
  • compile()
  • compile_auto()
  • compile_diagram()
  • build_execution_plan()
  • warn_shared_seeds()
  • NOMINAL
  • EXTERNAL_INPUT
  • INTERNAL_SIGNAL
  • PortOperation
  • StateOperation
  • ExecutionPlan
  • COMPILE_BACKENDS
  • SIMULATOR_BACKENDS
  • TRANSCRIPTION_BACKENDS
  • normalize_backend()
  • array_module()
  • jax_installed()
  • require_jax()
  • require_jax_numpy()
  • jax_x64_policy()
  • ensure_jax_x64()
  • configure_jax()
  • is_jax_key()
  • numpy_generator()
  • outputs_from_ports()
  • OutputEvaluator
  • DynamicsEvaluator
  • StepEvaluator
  • StaticEvaluator
  • gather_u()
  • StepRolloutMixin
  • IntegrationMixin
  • NumpyDynamicEvaluator
  • NumpyDiagramEvaluator
  • NumpyStaticEvaluator
  • NumpyStepEvaluator
  • NumpyStepDiagramEvaluator
  • JaxIntegrationMixin
  • JaxDynamicEvaluator
  • JaxDiagramEvaluator
  • JaxStaticEvaluator
  • JaxStepEvaluator
  • JaxStepDiagramEvaluator
• Simulation
  • Simulator
  • StaticSimulator
  • build_u_at_t()
  • SolverBackend
  • SciPySolverBackend
  • EulerSolverBackend
  • EulerFixedStepSolverBackend
  • RK4SolverBackend
  • Computer
  • StepSchedule
  • as_computer()
  • HybridSimulator
  • HybridSimResult
  • RealtimeSimulator
• Dynamics
  • StateSpaceSystem
  • LTISystem
  • MechanicalSystem
  • JaxMechanicalSystem
  • GeneralizedMechanicalSystem
  • Manipulator
  • Catalog
• Blocks
  • Integrator
  • Source
  • Step
  • Sine
  • WhiteNoise
  • TrajectorySource
  • TransferFunction
  • Lead
  • Lag
  • Error
  • Sum
  • Gain
  • Mux
  • Demux
  • Saturation
  • DeadZone
  • Relay
  • RateLimiter
  • LowPassFilter
  • NotchFilter
  • Washout
  • ZOHHold
  • NeuralNetwork
  • MLP
• Control
  • ImpedanceController
  • ImpedanceIntegralController
  • StateFeedbackController
  • OutputReferenceController
  • TimeVaryingStateFeedbackController
  • TrajectoryFeedbackController
  • plot_gain_schedule()
  • P
  • PID
  • PI
  • PD
  • ModelJointImpedance
  • JointImpedance()
  • TaskImpedance
  • TaskKinematic
  • TaskKinematicNullspace
  • ComputedTorqueController
  • SlidingModeController
  • lqr_gain()
  • place_gain()
  • lqr()
  • place()
  • lqg()
  • lqr_gain_schedule()
  • lqr_finite_horizon()
  • trajectory_lqr()
  • MIN_REACH
  • PurePursuit
  • is_closed()
  • NeuralPolicyController
  • angle_features()
  • ModelPredictiveController()
  • Command
  • ModelPredictiveControllerMixin
  • MPCStatelessController
  • MPCStatefulController
  • MPCTickSolve
  • MPCTickLatch
  • export_mpc_to_computer()
  • export_mpc_dual_rate_computer()
  • MPCBroadcastController
  • validate_mpc_planner()
  • mpc_warm_start_guess()
  • warm_start_guess_from_prev_plan()
  • mpc_default_computer_x0()
  • NominalCache
  • build_nominal_cache()
  • eval_signal()
  • mpc_animation_overlays()
  • mpc_plans_from_rollout()
• Estimation
  • StateObserver
  • luenberger_gain()
  • kalman_gain()
  • luenberger()
  • kalman()
• Analysis
  • linearize_matrices()
  • linearize()
  • design_model()
  • jacobian()
  • discretize()
  • DiscretizedDynamicSystem
  • DiscretizedEulerDynamicSystem
  • DiscretizedRK4DynamicSystem
  • controllability_matrix()
  • observability_matrix()
  • controllability()
  • observability()
  • StructuralResult
  • find_equilibrium()
  • modal_analysis()
  • animate_modal()
  • poles()
  • zeros()
  • gain()
  • frequency_response()
  • frequency_range()
  • minreal()
  • Margins
  • margins()
  • closed_loop_poles()
  • root_locus()
  • step_response()
  • settling_horizon()
  • care()
  • hamiltonian_matrix()
  • riccati_transition()
  • riccati_step()
  • riccati_map()
  • StepInfo
  • step_response()
  • step_info()
  • plot_step_response()
  • frequency_response()
  • bode()
  • margins()
  • nyquist()
  • pzmap()
  • root_locus()
  • transfer_function()
  • plot_bode()
  • plot_pzmap()
  • plot_root_locus()
  • plot_nyquist()
  • sensitivity()
  • complementary_sensitivity()
  • load_sensitivity()
  • noise_sensitivity()
  • METHODS
  • region_of_attraction()
  • LyapunovCertificate
  • VerificationReport
  • plot_region_of_attraction()
  • EVEN
• Optimization
  • MathematicalProgram
  • OptimizationResult
  • Optimizer
  • MathematicalProgramEvaluator
  • NumpyMathematicalProgramEvaluator
  • JaxMathematicalProgramEvaluator
  • OptimizerBackend
  • scipy_constraints_of()
  • ScipyMinimizeOptimizer
• Planning
  • PlanningProblem
  • StochasticPlanningProblem
  • ProblemParameters
  • as_stochastic()
  • Planner
  • PlanningSolution
  • compare()
  • Comparison
  • plot_cost_to_go()
  • sample_cost_to_go()
  • MonteCarloEvaluator
  • Evaluation
  • score_trajectory()
  • nominal_trajectory()
  • default_initial_trajectory()
  • mechanical_cubic_initial_trajectory()
  • linear_initial_trajectory()
  • TrajectoryOptimizationPlanner
  • TrajectoryOptimizationOptions
  • TrajectoryOptimizationRecord
  • TrajectoryOptimizationIteration
  • require_online_params()
  • Transcription
  • FixedGridOptions
  • trajectory_cost()
  • running_cost_samples()
  • trapezoid_integral()
  • trapezoidal_defect()
  • rk4_step_between_knots()
  • DirectCollocationOptions
  • DirectCollocationTranscription
  • MultipleShootingOptions
  • MultipleShootingTranscription
  • Spatial
  • Search
  • Policy synthesis
  • Reinforcement learning
• Graphical
  • SignalTrace
  • SignalPlotSpec
  • LivePlotHandle
  • resolve_plot_signals()
  • build_signal_plot_spec()
  • plot_time_signals()
  • open_time_signal_plot()
  • plot_phase_plane()
  • build_phase_plane_spec()
  • PhasePlaneSpec
  • PhasePlaneTrajectoryOverlay
  • render_phase_plane_matplotlib()
  • render_phase_plane_plotly()
  • build_diagram_topology()
  • expand_nested_diagrams()
  • abstract_boundary_ports()
  • DiagramTopology
  • TopologyNode
  • TopologyPort
  • TopologyEdge
  • BoundaryPortRef
  • TopologyCluster
  • TopologyExporter
  • export_diagram_topology()
  • Animator
  • AnimationRenderer
  • MatplotlibRenderer
  • MeshcatRenderer
  • PlotlyRenderer
  • PygameRenderer
  • make_renderer()
  • GraphicPrimitive
  • CustomLine
  • Point
  • Circle
  • Sphere
  • Rod
  • Plane
  • Box
  • ExtrudedPolygon
  • Arrow
  • TorqueArrow
  • HorizonPolyline
  • TrajectoryPolyline
  • arrow_pts()
  • torque_arc_pts()
  • camera_matrix()
  • world_to_camera()
  • ground_line()
  • spring_line()
  • wheel_box()
  • vehicle_body()
  • bounding_points()
  • bounding_radius()
  • AnimationRenderer
  • plot_input_output_map()
  • plot_control_law()
  • SweepAxis
  • PortMapSpec
  • render_port_map_matplotlib()
  • ControlFigure
  • Note
  • Panel
  • RefLine
  • Trace
  • render_control_figure()
  • Graphical catalog