trajectory_optimization_test.py

import math
import unittest
import warnings

import numpy as np

from pydrake.examples import PendulumPlant
from pydrake.math import eq, BsplineBasis
from pydrake.planning import (
    AddDirectCollocationConstraint,
    DirectCollocation,
    DirectCollocationConstraint,
    DirectTranscription,
    GcsTrajectoryOptimization,
    KinematicTrajectoryOptimization,
)
from pydrake.geometry.optimization import (
    GraphOfConvexSetsOptions,
    HPolyhedron,
    Point,
    VPolytope,
)
from pydrake.trajectories import (
    BsplineTrajectory,
    CompositeTrajectory,
    PiecewisePolynomial,
)
import pydrake.solvers as mp
from pydrake.symbolic import Variable
from pydrake.systems.framework import InputPortSelection
from pydrake.systems.primitives import LinearSystem
from pydrake.trajectories import PiecewisePolynomial, BsplineTrajectory
from pydrake.symbolic import Variable
from pydrake.systems.framework import InputPortSelection
from pydrake.systems.primitives import LinearSystem


def GurobiOrMosekSolverAvailable():
    return (mp.MosekSolver().available() and mp.MosekSolver().enabled()) or (
        mp.GurobiSolver().available() and mp.GurobiSolver().enabled())


class TestTrajectoryOptimization(unittest.TestCase):
    def test_direct_collocation(self):
        plant = PendulumPlant()
        context = plant.CreateDefaultContext()

        num_time_samples = 21
        dircol = DirectCollocation(
            plant,
            context,
            num_time_samples=num_time_samples,
            minimum_timestep=0.2,
            maximum_timestep=0.5,
            input_port_index=InputPortSelection.kUseFirstInputIfItExists,
            assume_non_continuous_states_are_fixed=False)
        prog = dircol.prog()
        num_initial_vars = prog.num_vars()

        # Spell out most of the methods, regardless of whether they make sense
        # as a consistent optimization.  The goal is to check the bindings,
        # not the implementation.
        t = dircol.time()
        dt = dircol.timestep(index=0)
        x = dircol.state()
        x2 = dircol.state(index=2)
        x0 = dircol.initial_state()
        xf = dircol.final_state()
        u = dircol.input()
        u2 = dircol.input(index=2)
        v = dircol.NewSequentialVariable(rows=1, name="test")
        v2 = dircol.GetSequentialVariableAtIndex(name="test", index=2)

        dircol.AddRunningCost(x.dot(x))
        input_con = dircol.AddConstraintToAllKnotPoints(u[0] == 0)
        self.assertEqual(len(input_con), 21)
        interval_bound = dircol.AddTimeIntervalBounds(
            lower_bound=0.3, upper_bound=0.4)
        self.assertIsInstance(interval_bound.evaluator(),
                              mp.BoundingBoxConstraint)
        equal_time_con = dircol.AddEqualTimeIntervalsConstraints()
        self.assertEqual(len(equal_time_con), 19)
        duration_bound = dircol.AddDurationBounds(
            lower_bound=0.3*21, upper_bound=0.4*21)
        self.assertIsInstance(duration_bound.evaluator(), mp.LinearConstraint)
        final_cost = dircol.AddFinalCost(2*x.dot(x))
        self.assertIsInstance(final_cost.evaluator(), mp.Cost)

        initial_u = PiecewisePolynomial.ZeroOrderHold([0, 0.3*21],
                                                      np.zeros((1, 2)))
        initial_x = PiecewisePolynomial()
        dircol.SetInitialTrajectory(traj_init_u=initial_u,
                                    traj_init_x=initial_x)

        was_called = dict(
            input=False,
            state=False,
            complete=False
        )

        def input_callback(t, u):
            was_called["input"] = True

        def state_callback(t, x):
            was_called["state"] = True

        def complete_callback(t, x, u, v):
            was_called["complete"] = True

        dircol.AddInputTrajectoryCallback(callback=input_callback)
        dircol.AddStateTrajectoryCallback(callback=state_callback)
        dircol.AddCompleteTrajectoryCallback(callback=complete_callback,
                                             names=["test"])

        result = mp.Solve(dircol.prog())
        self.assertTrue(was_called["input"])
        self.assertTrue(was_called["state"])
        self.assertTrue(was_called["complete"])

        dircol.GetSampleTimes(result=result)
        dircol.GetInputSamples(result=result)
        dircol.GetStateSamples(result=result)
        dircol.GetSequentialVariableSamples(result=result, name="test")
        dircol.ReconstructInputTrajectory(result=result)
        dircol.ReconstructStateTrajectory(result=result)

        constraint = DirectCollocationConstraint(plant, context)
        AddDirectCollocationConstraint(constraint, dircol.timestep(0),
                                       dircol.state(0), dircol.state(1),
                                       dircol.input(0), dircol.input(1),
                                       prog)

        # Test AddConstraintToAllKnotPoints variants.
        nc = len(prog.bounding_box_constraints())
        c = dircol.AddConstraintToAllKnotPoints(
            constraint=mp.BoundingBoxConstraint([0], [1]), vars=u)
        self.assertIsInstance(c[0], mp.Binding[mp.BoundingBoxConstraint])
        self.assertEqual(len(prog.bounding_box_constraints()),
                         nc + num_time_samples)
        nc = len(prog.linear_equality_constraints())
        c = dircol.AddConstraintToAllKnotPoints(
            constraint=mp.LinearEqualityConstraint([1], [0]), vars=u)
        self.assertIsInstance(c[0], mp.Binding[mp.LinearEqualityConstraint])
        self.assertEqual(len(prog.linear_equality_constraints()),
                         nc + num_time_samples)
        nc = len(prog.linear_constraints())
        c = dircol.AddConstraintToAllKnotPoints(
            constraint=mp.LinearConstraint([1], [0], [1]), vars=u)
        self.assertIsInstance(c[0], mp.Binding[mp.LinearConstraint])
        self.assertEqual(len(prog.linear_constraints()), nc + num_time_samples)
        nc = len(prog.linear_equality_constraints())
        # eq(x, 2) produces a 2-dimensional vector of Formula.
        c = dircol.AddConstraintToAllKnotPoints(eq(x, 2))
        self.assertIsInstance(c[0].evaluator(), mp.LinearEqualityConstraint)
        self.assertEqual(len(prog.linear_equality_constraints()),
                         nc + 2*num_time_samples)

        # Add a second direct collocation problem to the same prog.
        num_vars = prog.num_vars()
        dircol2 = DirectCollocation(
            plant,
            context,
            num_time_samples=num_time_samples,
            minimum_timestep=0.2,
            maximum_timestep=0.5,
            input_port_index=InputPortSelection.kUseFirstInputIfItExists,
            assume_non_continuous_states_are_fixed=False,
            prog=prog)
        self.assertEqual(dircol.prog(), dircol2.prog())
        self.assertEqual(prog.num_vars(), num_vars + num_initial_vars)

    def test_direct_transcription(self):
        # Integrator.
        plant = LinearSystem(
            A=[0.0], B=[1.0], C=[1.0], D=[0.0], time_period=0.1)
        context = plant.CreateDefaultContext()

        # Constructor for discrete systems.
        dirtran = DirectTranscription(plant, context, num_time_samples=21)

        # Spell out most of the methods, regardless of whether they make sense
        # as a consistent optimization.  The goal is to check the bindings,
        # not the implementation.
        t = dirtran.time()
        dt = dirtran.fixed_timestep()
        x = dirtran.state()
        x2 = dirtran.state(2)
        x0 = dirtran.initial_state()
        xf = dirtran.final_state()
        u = dirtran.input()
        u2 = dirtran.input(2)

        dirtran.AddRunningCost(x.dot(x))
        dirtran.AddConstraintToAllKnotPoints(u[0] == 0)
        dirtran.AddFinalCost(2*x.dot(x))

        initial_u = PiecewisePolynomial.ZeroOrderHold([0, 0.3*21],
                                                      np.zeros((1, 2)))
        initial_x = PiecewisePolynomial()
        dirtran.SetInitialTrajectory(initial_u, initial_x)

        result = mp.Solve(dirtran.prog())
        times = dirtran.GetSampleTimes(result)
        inputs = dirtran.GetInputSamples(result)
        states = dirtran.GetStateSamples(result)
        input_traj = dirtran.ReconstructInputTrajectory(result)
        state_traj = dirtran.ReconstructStateTrajectory(result)

        # Confirm that the constructor for continuous systems works (and
        # confirm binding of nested TimeStep).
        plant = LinearSystem(
            A=[0.0], B=[1.0], C=[1.0], D=[0.0], time_period=0.0)
        context = plant.CreateDefaultContext()
        dirtran = DirectTranscription(
            plant, context, num_time_samples=21,
            fixed_timestep=DirectTranscription.TimeStep(0.1))

    def test_kinematic_trajectory_optimization(self):
        trajopt = KinematicTrajectoryOptimization(num_positions=2,
                                                  num_control_points=10,
                                                  spline_order=3,
                                                  duration=2.0)
        self.assertIsInstance(trajopt.prog(), mp.MathematicalProgram)
        self.assertIsInstance(trajopt.get_mutable_prog(),
                              mp.MathematicalProgram)
        self.assertEqual(trajopt.num_positions(), 2)
        self.assertEqual(trajopt.num_control_points(), 10)
        self.assertIsInstance(trajopt.basis(), BsplineBasis)
        self.assertEqual(trajopt.basis().order(), 3)
        self.assertEqual(trajopt.control_points().shape, (2, 10))
        self.assertIsInstance(trajopt.duration(), Variable)
        self.assertEqual(trajopt.prog().GetInitialGuess(trajopt.duration()),
                         2.0)

        b = np.zeros((2, 1))
        trajopt.AddPathPositionConstraint(lb=b, ub=b, s=0)
        con = mp.LinearConstraint(np.eye(2), lb=b, ub=b)
        trajopt.AddPathPositionConstraint(con, 0)
        trajopt.AddPathVelocityConstraint(lb=b, ub=b, s=0)
        velocity_constraint = mp.LinearConstraint(np.eye(4),
                                                  lb=np.zeros((4, 1)),
                                                  ub=np.zeros((4, 1)))
        trajopt.AddVelocityConstraintAtNormalizedTime(velocity_constraint, s=0)
        trajopt.AddPathAccelerationConstraint(lb=b, ub=b, s=0)
        trajopt.AddDurationConstraint(1, 1)
        trajopt.AddPositionBounds(lb=b, ub=b)
        trajopt.AddVelocityBounds(lb=b, ub=b)
        trajopt.AddAccelerationBounds(lb=b, ub=b)
        trajopt.AddJerkBounds(lb=b, ub=b)

        trajopt.AddDurationCost(weight=1)
        trajopt.AddPathLengthCost(weight=1)

        result = mp.Solve(trajopt.prog())
        q = trajopt.ReconstructTrajectory(result=result)
        self.assertIsInstance(q, BsplineTrajectory)
        trajopt.SetInitialGuess(trajectory=q)

    def test_gcs_trajectory_optimization_2d(self):
        """The following 2D environment has been presented in the GCS paper.

        We have two possible starts, S1 and S2, and two possible goals,
        G1 and G2. The goal is to find a the shortest path from either of
        the starts to either of the goals while avoiding the obstacles.
        Further we constraint the path to go through either the intermediate
        point I or the subspace.

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        """

        dimension = 2
        gcs = GcsTrajectoryOptimization(num_positions=dimension)
        self.assertEqual(gcs.num_positions(), dimension)

        # Define the collision free space.
        vertices = [
            np.array([[0.4, 0.4, 0.0, 0.0], [0.0, 5.0, 5.0, 0.0]]),
            np.array([[0.4, 1.0, 1.0, 0.4], [2.4, 2.4, 2.6, 2.6]]),
            np.array([[1.4, 1.4, 1.0, 1.0], [2.2, 4.6, 4.6, 2.2]]),
            np.array([[1.4, 2.4, 2.4, 1.4], [2.2, 2.6, 2.8, 2.8]]),
            np.array([[2.2, 2.4, 2.4, 2.2], [2.8, 2.8, 4.6, 4.6]]),
            np.array([[1.4, 1.0, 1.0, 3.8, 3.8], [2.2, 2.2, 0.0, 0.0, 0.2]]),
            np.array([[3.8, 3.8, 1.0, 1.0], [4.6, 5.0, 5.0, 4.6]]),
            np.array([[5.0, 5.0, 4.8, 3.8, 3.8], [0.0, 1.2, 1.2, 0.2, 0.0]]),
            np.array([[3.4, 4.8, 5.0, 5.0], [2.6, 1.2, 1.2, 2.6]]),
            np.array([[3.4, 3.8, 3.8, 3.4], [2.6, 2.6, 4.6, 4.6]]),
            np.array([[3.8, 4.4, 4.4, 3.8], [2.8, 2.8, 3.0, 3.0]]),
            np.array([[5.0, 5.0, 4.4, 4.4], [2.8, 5.0, 5.0, 2.8]])
        ]

        max_vel = np.ones((2, 1))

        # We add a path length cost to the entire graph.
        # This can be called ahead of time or after adding the regions.
        gcs.AddPathLengthCost(weight=1.0)
        # This cost is equivalent to the above.
        # It will be added twice, which is unnecessary,
        # but we do it to test the binding.
        gcs.AddPathLengthCost(weight_matrix=np.eye(dimension))

        # Add a mimimum time cost to the entire graph.
        gcs.AddTimeCost(weight=1.0)
        # Add the cost again, which is unnecessary for the optimization
        # but useful to check the binding with the default values.
        gcs.AddTimeCost()

        # Add velocity bounds to the entire graph.
        gcs.AddVelocityBounds(-max_vel, max_vel)

        # Add two subgraphs with different orders.
        main1 = gcs.AddRegions(
            regions=[HPolyhedron(VPolytope(v)) for v in vertices],
            order=1,
            name="main1")
        self.assertIsInstance(main1, GcsTrajectoryOptimization.Subgraph)
        self.assertEqual(main1.order(), 1)
        self.assertEqual(main1.name(), "main1")
        self.assertEqual(main1.size(), len(vertices))
        self.assertIsInstance(main1.regions(), list)
        self.assertIsInstance(main1.regions()[0], HPolyhedron)

        # This adds the edges manually.
        # Doing this is much faster since it avoids computing
        # pairwise set intersection checks.
        main2 = gcs.AddRegions(
            regions=[HPolyhedron(VPolytope(v)) for v in vertices],
            edges_between_regions=[(0, 1), (1, 0), (1, 2), (2, 1), (2, 3),
                                   (3, 2), (2, 5), (5, 2), (2, 6), (6, 2),
                                   (3, 4), (4, 3), (3, 5), (5, 3), (4, 6),
                                   (6, 4), (5, 7), (7, 5), (6, 9), (9, 6),
                                   (7, 8), (8, 7), (8, 9), (9, 8), (9, 10),
                                   (10, 9), (10, 11), (11, 10)],
            order=3,
            name="main2")

        self.assertIsInstance(main2, GcsTrajectoryOptimization.Subgraph)
        self.assertEqual(main2.order(), 3)
        self.assertEqual(main2.name(), "main2")
        self.assertEqual(main2.size(), len(vertices))
        self.assertIsInstance(main2.regions(), list)
        self.assertIsInstance(main2.regions()[0], HPolyhedron)

        # Add two start and goal regions.
        start1 = np.array([0.2, 0.2])
        start2 = np.array([0.3, 3.2])

        goal1 = np.array([4.8, 4.8])
        goal2 = np.array([4.9, 2.4])

        source = gcs.AddRegions([Point(start1), Point(start2)],
                                order=0,
                                name="starts")
        self.assertIsInstance(source, GcsTrajectoryOptimization.Subgraph)
        self.assertEqual(source.order(), 0)
        self.assertEqual(source.name(), "starts")
        self.assertEqual(source.size(), 2)
        self.assertIsInstance(source.regions(), list)
        self.assertIsInstance(source.regions()[0], Point)

        # Here we force a delay of 10 seconds at the goal.
        target = gcs.AddRegions(regions=[Point(goal1),
                                         Point(goal2)],
                                order=0,
                                h_min=10,
                                h_max=10,
                                name='goals')
        self.assertIsInstance(target, GcsTrajectoryOptimization.Subgraph)
        self.assertEqual(target.order(), 0)
        self.assertEqual(target.name(), "goals")
        self.assertEqual(target.size(), 2)
        self.assertIsInstance(target.regions(), list)
        self.assertIsInstance(target.regions()[0], Point)

        # We connect the subgraphs main1 and main2 by constraining it to
        # go through either of the subspaces.
        subspace_region = HPolyhedron(VPolytope(vertices[7]))
        subspace_point = Point([2.3, 3.5])

        self.assertIsInstance(
            gcs.AddEdges(from_subgraph=main1,
                         to_subgraph=main2,
                         subspace=subspace_point),
            GcsTrajectoryOptimization.EdgesBetweenSubgraphs)
        self.assertIsInstance(
            gcs.AddEdges(main1, main2, subspace=subspace_region),
            GcsTrajectoryOptimization.EdgesBetweenSubgraphs)

        # We connect the start and goal regions to the rest of the graph.
        self.assertIsInstance(gcs.AddEdges(source, main1),
                              GcsTrajectoryOptimization.EdgesBetweenSubgraphs)
        self.assertIsInstance(gcs.AddEdges(main2, target),
                              GcsTrajectoryOptimization.EdgesBetweenSubgraphs)

        # This weight matrix penalizes movement in the y direction three
        # times more than in the x direction only for the main2 subgraph.
        main2.AddPathLengthCost(weight_matrix=np.diag([1.0, 3.0]))

        # Adding this cost checks the python binding. It won't contribute to
        # the solution since we already added the minimum time cost to the
        # whole graph.
        main2.AddTimeCost(weight=1.0)
        # Add the cost again, which is unnecessary for the optimization
        # but useful to check the binding with the default values.
        main2.AddTimeCost()

        # Add tighter velocity bounds to the main2 subgraph.
        main2.AddVelocityBounds(lb=-0.5*max_vel, ub=0.5*max_vel)

        options = GraphOfConvexSetsOptions()
        options.convex_relaxation = True
        options.max_rounded_paths = 5

        if not GurobiOrMosekSolverAvailable():
            return

        traj, result = gcs.SolvePath(source=source,
                                     target=target,
                                     options=options)

        self.assertIsInstance(result, mp.MathematicalProgramResult)
        self.assertIsInstance(traj, CompositeTrajectory)
        self.assertTrue(result.is_success())
        self.assertEqual(traj.rows(), dimension)

        np.testing.assert_array_almost_equal(traj.value(traj.start_time()),
                                             start2[:, None], 6)
        np.testing.assert_array_almost_equal(traj.value(traj.end_time()),
                                             goal2[:, None], 6)

        # Check that the delay at the goal is respected.
        np.testing.assert_array_almost_equal(traj.value(traj.end_time() - 10),
                                             goal2[:, None], 6)
        self.assertTrue(traj.end_time() - traj.start_time() >= 10)

        self.assertIsInstance(
            gcs.GetGraphvizString(result=result,
                                  show_slack=True,
                                  precision=3,
                                  scientific=False), str)