Пример #1
0
def solve_extrusion(robot, obstacles, element_from_id, node_points, element_bodies, extrusion_path, ground_nodes, args,
                    partial_orders=[], precompute=False, **kwargs):
    # TODO: could treat ground as partial orders
    backtrack_limit = INF # 0 | INF
    seed = hash((time.time(), args.seed))
    set_numpy_seed(seed)
    set_random_seed(seed)

    # initial_position = point_from_pose(get_link_pose(robot, link_from_name(robot, TOOL_LINK)))
    # elements = sorted(element_bodies.keys())
    # sequence = plan_stiffness(extrusion_path, element_from_id, node_points, ground_nodes, elements,
    #                           initial_position=initial_position, max_time=INF, max_backtrack=INF)
    # if has_gui():
    #     draw_ordered(sequence, node_points)
    #     wait_for_user()
    # return

    initial_conf = get_configuration(robot)
    if args.algorithm == 'stripstream':
        sampled_trajectories = []
        if precompute:
            sampled_trajectories = sample_trajectories(robot, obstacles, node_points, element_bodies, ground_nodes)
        plan, data = stripstream(robot, obstacles, node_points, element_bodies, ground_nodes,
                                 trajectories=sampled_trajectories, collisions=not args.cfree,
                                 max_time=args.max_time, disable=args.disable, **kwargs)
    elif args.algorithm == 'progression':
        plan, data = progression(robot, obstacles, element_bodies, extrusion_path, partial_orders=partial_orders,
                                 heuristic=args.bias, max_time=args.max_time,
                                 backtrack_limit=backtrack_limit, collisions=not args.cfree,
                                 disable=args.disable, stiffness=args.stiffness, motions=args.motions, **kwargs)
    elif args.algorithm == 'regression':
        plan, data = regression(robot, obstacles, element_bodies, extrusion_path, partial_orders=partial_orders,
                                heuristic=args.bias, max_time=args.max_time,
                                backtrack_limit=backtrack_limit, collisions=not args.cfree,
                                disable=args.disable, stiffness=args.stiffness, motions=args.motions, **kwargs)
    elif args.algorithm == 'lookahead':
        plan, data = lookahead(robot, obstacles, element_bodies, extrusion_path,
                               partial_orders=partial_orders, heuristic=args.bias,
                               max_time=args.max_time, backtrack_limit=backtrack_limit,
                               ee_only=args.ee_only, collisions=not args.cfree,
                               disable=args.disable, stiffness=args.stiffness, motions=args.motions, **kwargs)
    else:
        raise ValueError(args.algorithm)
    if args.motions:
        plan = compute_motions(robot, obstacles, element_bodies, initial_conf, plan, collisions=not args.cfree)
    return plan, data
Пример #2
0
def regression(robot,
               obstacles,
               element_bodies,
               extrusion_path,
               partial_orders=[],
               heuristic='z',
               max_time=INF,
               max_memory=INF,
               backtrack_limit=INF,
               revisit=False,
               stiffness_attempts=1,
               collisions=True,
               stiffness=True,
               motions=True,
               lazy=LAZY,
               checker=None,
               **kwargs):
    # Focused has the benefit of reusing prior work
    # Greedy has the benefit of conditioning on previous choices
    # TODO: max branching factor
    # TODO: be more careful when near the end
    # TODO: max time spent evaluating successors (less expensive when few left)
    # TODO: tree rollouts
    # TODO: best-first search with a minimizing path distance cost
    # TODO: immediately select if becomes more stable
    # TODO: focus branching factor on most stable regions

    start_time = time.time()
    initial_conf = get_configuration(robot)
    initial_position = get_tool_position(robot)
    element_from_id, node_points, ground_nodes = load_extrusion(extrusion_path)
    id_from_element = get_id_from_element(element_from_id)
    all_elements = frozenset(element_bodies)
    ground_elements = get_ground_elements(all_elements, ground_nodes)
    if stiffness and (checker is None):
        checker = create_stiffness_checker(extrusion_path, verbose=False)
    print_gen_fn = get_print_gen_fn(robot,
                                    obstacles,
                                    node_points,
                                    element_bodies,
                                    ground_nodes,
                                    precompute_collisions=False,
                                    max_directions=MAX_DIRECTIONS,
                                    max_attempts=MAX_ATTEMPTS,
                                    collisions=collisions,
                                    **kwargs)
    heuristic_fn = get_heuristic_fn(robot,
                                    extrusion_path,
                                    heuristic,
                                    checker=checker,
                                    forward=False)

    queue = []
    outgoing_from_element = outgoing_from_edges(partial_orders)

    def add_successors(printed, position, conf):
        only_ground = printed <= ground_elements
        num_remaining = len(printed) - 1
        #assert 0 <= num_remaining
        for element in randomize(printed):
            if not (outgoing_from_element[element] & printed) and implies(
                    is_ground(element, ground_nodes), only_ground):
                for directed in get_directions(element):
                    visits = 0
                    bias = heuristic_fn(printed, directed, position, conf)
                    priority = (num_remaining, bias, random.random())
                    heapq.heappush(queue,
                                   (visits, priority, printed, directed, conf))

    final_conf = initial_conf  # TODO: allow choice of final config
    final_position = initial_position
    final_printed = all_elements
    visited = {final_printed: Node(None, None)}
    if check_connected(ground_nodes, final_printed) and \
            (not stiffness or test_stiffness(extrusion_path, element_from_id, final_printed, checker=checker)):
        add_successors(final_printed, final_position, final_conf)

    # if has_gui():
    #     sequence = sorted(final_printed, key=lambda e: heuristic_fn(final_printed, e, conf=None), reverse=True)
    #     remove_all_debug()
    #     draw_ordered(sequence, node_points)
    #     wait_for_user()

    plan = None
    min_remaining = len(all_elements)
    num_evaluated = max_backtrack = extrusion_failures = transit_failures = stiffness_failures = 0
    while queue and (elapsed_time(start_time) <
                     max_time) and check_memory():  #max_memory):
        visits, priority, printed, directed, current_conf = heapq.heappop(
            queue)
        element = get_undirected(all_elements, directed)
        num_remaining = len(printed)
        backtrack = num_remaining - min_remaining
        max_backtrack = max(max_backtrack, backtrack)
        if backtrack_limit < backtrack:
            break  # continue
        num_evaluated += 1

        print(
            'Iteration: {} | Best: {} | Printed: {} | Element: {} | Index: {} | Time: {:.3f}'
            .format(num_evaluated, min_remaining, len(printed), element,
                    id_from_element[element], elapsed_time(start_time)))
        next_printed = printed - {element}
        next_nodes = compute_printed_nodes(ground_nodes, next_printed)

        #draw_action(node_points, next_printed, element)
        #if 3 < backtrack + 1:
        #    remove_all_debug()
        #    set_renderer(enable=True)
        #    draw_model(next_printed, node_points, ground_nodes)
        #    wait_for_user()

        node1, node2 = directed
        if (next_printed
                in visited) or (node1
                                not in next_nodes) or not check_connected(
                                    ground_nodes, next_printed):
            continue
        # TODO: stiffness plan lazily here possibly with reuse
        if stiffness and not test_stiffness(
                extrusion_path, element_from_id, next_printed,
                checker=checker):
            stiffness_failures += 1
            continue
        # TODO: stronger condition for this procedure
        # if plan_stiffness(extrusion_path, element_from_id, node_points, ground_nodes, next_printed,
        #                   checker=checker, max_backtrack=0) is None:
        #     # TODO: cache and reuse prior stiffness plans
        #     print('Failed stiffness plan') # TODO: require just a short horizon
        #     continue
        if revisit:
            heapq.heappush(
                queue, (visits + 1, priority, printed, directed, current_conf))

        command, = next(print_gen_fn(node1, element, extruded=next_printed),
                        (None, ))
        if command is None:
            extrusion_failures += 1
            continue
        if motions and not lazy:
            motion_traj = compute_motion(
                robot,
                obstacles,
                element_bodies,
                printed,
                command.end_conf,
                current_conf,
                collisions=collisions,
                max_time=max_time -
                elapsed_time(start_time))  # TODO: smooth=...)
            if motion_traj is None:
                transit_failures += 1
                continue
            command.trajectories.append(motion_traj)

        if num_remaining < min_remaining:
            min_remaining = num_remaining
            #print('New best: {}'.format(num_remaining))
            #if has_gui():
            #    # TODO: change link transparency
            #    remove_all_debug()
            #    draw_model(next_printed, node_points, ground_nodes)
            #    wait_for_duration(0.5)

        visited[next_printed] = Node(
            command, printed)  # TODO: be careful when multiple trajs
        if not next_printed:
            min_remaining = 0
            commands = retrace_commands(visited, next_printed, reverse=True)
            if OPTIMIZE:
                commands = optimize_commands(robot,
                                             obstacles,
                                             element_bodies,
                                             extrusion_path,
                                             initial_conf,
                                             commands,
                                             motions=motions,
                                             collisions=collisions)
            plan = flatten_commands(commands)
            if motions and not lazy:
                motion_traj = compute_motion(robot,
                                             obstacles,
                                             element_bodies,
                                             frozenset(),
                                             initial_conf,
                                             plan[0].start_conf,
                                             collisions=collisions,
                                             max_time=max_time -
                                             elapsed_time(start_time))
                if motion_traj is None:
                    plan = None
                    transit_failures += 1
                else:
                    plan.insert(0, motion_traj)
            if motions and lazy:
                plan = compute_motions(robot,
                                       obstacles,
                                       element_bodies,
                                       initial_conf,
                                       plan,
                                       collisions=collisions,
                                       max_time=max_time -
                                       elapsed_time(start_time))
            break
            # if plan is not None:
            #     break
        add_successors(next_printed, node_points[node1], command.start_conf)
    #del checker

    data = {
        #'memory': get_memory_in_kb(), # May need to update instead
        'num_evaluated': num_evaluated,
        'min_remaining': min_remaining,
        'max_backtrack': max_backtrack,
        'stiffness_failures': stiffness_failures,
        'extrusion_failures': extrusion_failures,
        'transit_failures': transit_failures,
    }
    return plan, data
Пример #3
0
def progression(robot,
                obstacles,
                element_bodies,
                extrusion_path,
                partial_orders=[],
                heuristic='z',
                max_time=INF,
                backtrack_limit=INF,
                revisit=False,
                stiffness=True,
                motions=True,
                collisions=True,
                lazy=LAZY,
                checker=None,
                **kwargs):

    start_time = time.time()
    initial_conf = get_configuration(robot)
    initial_position = get_tool_position(robot)
    element_from_id, node_points, ground_nodes = load_extrusion(extrusion_path)
    if checker is None:
        checker = create_stiffness_checker(extrusion_path, verbose=False)
    print_gen_fn = get_print_gen_fn(robot,
                                    obstacles,
                                    node_points,
                                    element_bodies,
                                    ground_nodes,
                                    precompute_collisions=False,
                                    collisions=collisions,
                                    **kwargs)
    id_from_element = get_id_from_element(element_from_id)
    all_elements = frozenset(element_bodies)
    heuristic_fn = get_heuristic_fn(robot,
                                    extrusion_path,
                                    heuristic,
                                    checker=checker,
                                    forward=True)

    initial_printed = frozenset()
    queue = []
    visited = {initial_printed: Node(None, None)}
    if check_connected(ground_nodes, all_elements) and \
            test_stiffness(extrusion_path, element_from_id, all_elements):
        add_successors(queue,
                       all_elements,
                       node_points,
                       ground_nodes,
                       heuristic_fn,
                       initial_printed,
                       initial_position,
                       initial_conf,
                       partial_orders=partial_orders)

    plan = None
    min_remaining = len(all_elements)
    num_evaluated = max_backtrack = stiffness_failures = extrusion_failures = transit_failures = 0
    while queue and (elapsed_time(start_time) < max_time):
        num_evaluated += 1
        visits, priority, printed, directed, current_conf = heapq.heappop(
            queue)
        element = get_undirected(all_elements, directed)
        num_remaining = len(all_elements) - len(printed)
        backtrack = num_remaining - min_remaining
        max_backtrack = max(max_backtrack, backtrack)
        if backtrack_limit < backtrack:
            break  # continue
        num_evaluated += 1
        if num_remaining < min_remaining:
            min_remaining = num_remaining
        print(
            'Iteration: {} | Best: {} | Printed: {} | Element: {} | Index: {} | Time: {:.3f}'
            .format(num_evaluated, min_remaining, len(printed), element,
                    id_from_element[element], elapsed_time(start_time)))
        next_printed = printed | {element}
        assert check_connected(ground_nodes, next_printed)
        if (next_printed in visited) or (stiffness and not test_stiffness(
                extrusion_path, element_from_id, next_printed, checker=checker)
                                         ):
            stiffness_failures += 1
            continue
        if revisit:  # could also prevent revisiting if command is not None
            heapq.heappush(
                queue, (visits + 1, priority, printed, directed, current_conf))

        node1, node2 = directed
        command, = next(print_gen_fn(node1, element, extruded=printed),
                        (None, ))
        if command is None:
            extrusion_failures += 1
            continue
        if motions and not lazy:
            # TODO: test reachability from initial_conf
            motion_traj = compute_motion(robot,
                                         obstacles,
                                         element_bodies,
                                         printed,
                                         current_conf,
                                         command.start_conf,
                                         collisions=collisions,
                                         max_time=max_time -
                                         elapsed_time(start_time))
            if motion_traj is None:
                transit_failures += 1
                continue
            command.trajectories.insert(0, motion_traj)

        visited[next_printed] = Node(command, printed)
        if all_elements <= next_printed:
            min_remaining = 0
            commands = retrace_commands(visited, next_printed)
            if OPTIMIZE:
                commands = optimize_commands(robot,
                                             obstacles,
                                             element_bodies,
                                             extrusion_path,
                                             initial_conf,
                                             commands,
                                             motions=motions,
                                             collisions=collisions)
            plan = flatten_commands(commands)
            if motions and not lazy:
                motion_traj = compute_motion(robot,
                                             obstacles,
                                             element_bodies,
                                             frozenset(),
                                             initial_conf,
                                             plan[0].start_conf,
                                             collisions=collisions,
                                             max_time=max_time -
                                             elapsed_time(start_time))
                if motion_traj is None:
                    plan = None
                    transit_failures += 1
                else:
                    plan.append(motion_traj)
            if motions and lazy:
                plan = compute_motions(robot,
                                       obstacles,
                                       element_bodies,
                                       initial_conf,
                                       plan,
                                       collisions=collisions,
                                       max_time=max_time -
                                       elapsed_time(start_time))
            break
            # if plan is not None:
            #     break
        add_successors(queue,
                       all_elements,
                       node_points,
                       ground_nodes,
                       heuristic_fn,
                       next_printed,
                       node_points[node2],
                       command.end_conf,
                       partial_orders=partial_orders)

    data = {
        'num_evaluated': num_evaluated,
        'min_remaining': min_remaining,
        'max_backtrack': max_backtrack,
        'stiffness_failures': stiffness_failures,
        'extrusion_failures': extrusion_failures,
        'transit_failures': transit_failures,
    }
    return plan, data
Пример #4
0
def lookahead(robot,
              obstacles,
              element_bodies,
              extrusion_path,
              partial_orders=[],
              num_ee=0,
              num_arm=1,
              plan_all=False,
              use_conflicts=False,
              use_replan=False,
              heuristic='z',
              max_time=INF,
              backtrack_limit=INF,
              revisit=False,
              ee_only=False,
              collisions=True,
              stiffness=True,
              motions=True,
              lazy=LAZY,
              checker=None,
              **kwargs):
    if not use_conflicts:
        num_ee, num_arm = min(num_ee, 1), min(num_arm, 1)
    if ee_only:
        num_ee, num_arm = max(num_arm, num_ee), 0
    print('#EE: {} | #Arm: {}'.format(num_ee, num_arm))
    # TODO: only check nearby remaining_elements
    # TODO: only check collisions conditioned on current decisions
    start_time = time.time()
    initial_conf = get_configuration(robot)
    initial_position = get_tool_position(robot)
    element_from_id, node_points, ground_nodes = load_extrusion(extrusion_path)
    if checker is None:
        checker = create_stiffness_checker(extrusion_path, verbose=False)

    #print_gen_fn = get_print_gen_fn(robot, obstacles, node_points, element_bodies, ground_nodes,
    #                                precompute_collisions=False, supports=False, ee_only=ee_only,
    #                                max_directions=MAX_DIRECTIONS, max_attempts=MAX_ATTEMPTS, collisions=collisions, **kwargs)
    full_print_gen_fn = get_print_gen_fn(robot,
                                         obstacles,
                                         node_points,
                                         element_bodies,
                                         ground_nodes,
                                         precompute_collisions=False,
                                         ee_only=ee_only,
                                         allow_failures=True,
                                         collisions=collisions,
                                         **kwargs)
    # TODO: could just check environment collisions & kinematics instead of element collisions
    ee_print_gen_fn = get_print_gen_fn(robot,
                                       obstacles,
                                       node_points,
                                       element_bodies,
                                       ground_nodes,
                                       precompute_collisions=False,
                                       ee_only=True,
                                       allow_failures=True,
                                       collisions=collisions,
                                       **kwargs)
    id_from_element = get_id_from_element(element_from_id)
    all_elements = frozenset(element_bodies)
    heuristic_fn = get_heuristic_fn(robot,
                                    extrusion_path,
                                    heuristic,
                                    checker=checker,
                                    forward=True)
    #distance_fn = get_distance_fn(robot, joints, weights=JOINT_WEIGHTS)
    # TODO: 2-step lookahead based on neighbors or spatial proximity

    full_sample_traj, full_trajs_from_element = get_sample_traj(
        ground_nodes, element_bodies, full_print_gen_fn, collisions=collisions)
    ee_sample_traj, ee_trajs_from_element = get_sample_traj(
        ground_nodes, element_bodies, ee_print_gen_fn, collisions=collisions)
    if ee_only:
        full_sample_traj = ee_sample_traj
    #ee_sample_traj, ee_trajs_from_element = full_sample_traj, full_trajs_from_element

    #heuristic_trajs_from_element = full_trajs_from_element if (num_ee == 0) else ee_trajs_from_element
    heuristic_trajs_from_element = full_trajs_from_element if (
        num_arm != 0) else ee_trajs_from_element

    #########################

    def sample_remaining(printed, next_printed, sample_fn, num=1, **kwargs):
        if num == 0:
            return True
        remaining_elements = (all_elements - next_printed) if plan_all else \
            compute_printable_elements(all_elements, ground_nodes, next_printed)
        # TODO: could just consider nodes in printed (connected=True)
        return all(
            sample_fn(printed,
                      next_printed,
                      element,
                      connected=False,
                      num=num,
                      **kwargs) for element in randomize(remaining_elements))

    def conflict_fn(printed, element, conf):
        # Dead-end detection without stability performs reasonably well
        # TODO: could add element if desired
        order = retrace_elements(visited, printed)
        printed = frozenset(
            order[:-1])  # Remove last element (to ensure at least one traj)
        if use_replan:
            remaining = list(all_elements - printed)
            requires_replan = [
                all(element in traj.colliding
                    for traj in ee_trajs_from_element[e2]
                    if not (traj.colliding & printed)) for e2 in remaining
                if e2 != element
            ]
            return len(requires_replan)
        else:
            safe_trajectories = [
                traj for traj in heuristic_trajs_from_element[element]
                if not (traj.colliding & printed)
            ]
            assert safe_trajectories
            best_traj = max(safe_trajectories,
                            key=lambda traj: len(traj.colliding))
            num_colliding = len(best_traj.colliding)
            return -num_colliding
        #distance = distance_fn(conf, best_traj.start_conf)
        # TODO: ee distance vs conf distance
        # TODO: l0 distance based on whether we remain at the same node
        # TODO: minimize instability while printing (dynamic programming)
        #return (-num_colliding, distance)

    if use_conflicts:
        priority_fn = lambda *args: (conflict_fn(*args), heuristic_fn(*args))
    else:
        priority_fn = heuristic_fn

    #########################

    initial_printed = frozenset()
    queue = []
    visited = {initial_printed: Node(None, None)}
    if check_connected(ground_nodes, all_elements) and \
            test_stiffness(extrusion_path, element_from_id, all_elements) and \
            sample_remaining(initial_printed, initial_printed, ee_sample_traj, num=num_ee) and \
            sample_remaining(initial_printed, initial_printed, full_sample_traj, num=num_arm):
        add_successors(queue,
                       all_elements,
                       node_points,
                       ground_nodes,
                       priority_fn,
                       initial_printed,
                       initial_position,
                       initial_conf,
                       partial_orders=partial_orders)

    plan = None
    min_remaining = INF
    num_evaluated = worst_backtrack = num_deadends = stiffness_failures = extrusion_failures = transit_failures = 0
    while queue and (elapsed_time(start_time) < max_time):
        num_evaluated += 1
        visits, priority, printed, directed, current_conf = heapq.heappop(
            queue)
        element = get_undirected(all_elements,
                                 directed)  # TODO: use the correct direction
        num_remaining = len(all_elements) - len(printed)
        backtrack = num_remaining - min_remaining
        worst_backtrack = max(worst_backtrack, backtrack)
        if backtrack_limit < backtrack:
            break  # continue
        num_evaluated += 1
        if num_remaining < min_remaining:
            min_remaining = num_remaining
        print(
            'Iteration: {} | Best: {} | Backtrack: {} | Deadends: {} | Printed: {} | Element: {} | Index: {} | Time: {:.3f}'
            .format(num_evaluated, min_remaining, worst_backtrack,
                    num_deadends, len(printed), element,
                    id_from_element[element], elapsed_time(start_time)))
        if has_gui():
            color_structure(element_bodies, printed, element)

        next_printed = printed | {element}
        if next_printed in visited:
            continue
        assert check_connected(ground_nodes, next_printed)
        if stiffness and not test_stiffness(extrusion_path,
                                            element_from_id,
                                            next_printed,
                                            checker=checker,
                                            verbose=False):
            # Hard dead-end
            #num_deadends += 1
            stiffness_failures += 1
            print('Partial structure is not stiff!')
            continue
        if revisit:
            heapq.heappush(
                queue, (visits + 1, priority, printed, element, current_conf))

        #condition = frozenset()
        #condition = set(retrace_elements(visited, printed, horizon=2))
        #condition = printed # horizon=1
        condition = next_printed

        if not sample_remaining(
                condition, next_printed, ee_sample_traj, num=num_ee):
            num_deadends += 1
            print('An end-effector successor could not be sampled!')
            continue

        print('Sampling transition')
        #command = sample_extrusion(print_gen_fn, ground_nodes, printed, element)
        command = next(
            iter(full_sample_traj(printed, printed, element, connected=True)),
            None)
        if command is None:
            # Soft dead-end
            print('The transition could not be sampled!')
            extrusion_failures += 1
            continue

        print('Sampling successors')
        if not sample_remaining(
                condition, next_printed, full_sample_traj, num=num_arm):
            num_deadends += 1
            print('A successor could not be sampled!')
            continue

        start_conf = end_conf = None
        if not ee_only:
            start_conf, end_conf = command.start_conf, command.end_conf
        if (start_conf is not None) and motions and not lazy:
            motion_traj = compute_motion(robot,
                                         obstacles,
                                         element_bodies,
                                         printed,
                                         current_conf,
                                         start_conf,
                                         collisions=collisions,
                                         max_time=max_time -
                                         elapsed_time(start_time))
            if motion_traj is None:
                transit_failures += 1
                continue
            command.trajectories.insert(0, motion_traj)

        visited[next_printed] = Node(command, printed)
        if all_elements <= next_printed:
            # TODO: anytime mode
            min_remaining = 0
            plan = retrace_trajectories(visited, next_printed)
            if motions and not lazy:
                motion_traj = compute_motion(robot,
                                             obstacles,
                                             element_bodies,
                                             frozenset(),
                                             initial_conf,
                                             plan[0].start_conf,
                                             collisions=collisions,
                                             max_time=max_time -
                                             elapsed_time(start_time))
                if motion_traj is None:
                    plan = None
                    transit_failures += 1
                else:
                    plan.append(motion_traj)
            if motions and lazy:
                plan = compute_motions(robot,
                                       obstacles,
                                       element_bodies,
                                       initial_conf,
                                       plan,
                                       collisions=collisions,
                                       max_time=max_time -
                                       elapsed_time(start_time))
            break
            # if plan is not None:
            #     break
        add_successors(queue,
                       all_elements,
                       node_points,
                       ground_nodes,
                       priority_fn,
                       next_printed,
                       node_points[directed[1]],
                       end_conf,
                       partial_orders=partial_orders)

    data = {
        'num_evaluated': num_evaluated,
        'min_remaining': min_remaining,
        'max_backtrack': worst_backtrack,
        'stiffness_failures': stiffness_failures,
        'extrusion_failures': extrusion_failures,
        'transit_failures': transit_failures,
        'num_deadends': num_deadends,
    }
    return plan, data