Lula [omni.isaac.lula]

Overview

The lula module provides a high-level interface to the Lula library, with classes exposing routines for forward and inverse kinematics, sampling-based global planning, and smooth reactive motion generation via RMPflow and geometric fabrics.

Logging

class LogLevel

Logging levels, ordered from least to most verbose.

FATAL

Logging level for nonrecoverable errors (minimum level, so always enabled).

ERROR

Logging level for recoverable errors.

WARNING

Logging level for warnings, indicating possible cause for concern.

INFO

Logging level for informational messages.

VERBOSE

Logging level for highly verbose informational messages.

set_log_level(level: lula.LogLevel = LogLevel.ERROR) → None

Suppress output for all log messages with associated verbosity higher than log_level.

Rotations and Poses

class Rotation3

Representation of a rotation (i.e. element of SO(3)) in 3D.

distance(rotation0: lula.Rotation3, rotation1: lula.Rotation3) → float

Compute the minimum angular distance (in radians) between two rotations.

from_scaled_axis(scaled_axis: numpy.ndarray[float64[3, 1]]) → lula.Rotation3

Construct a rotation from a scaled axis, where the magnitude of scaled_axis represents the rotation angle in radians.

identity() → lula.Rotation3

Create identity rotation.

inverse(self: lula.Rotation3) → lula.Rotation3

Returns the inverse rotation.

matrix(self: lula.Rotation3) → numpy.ndarray[float64[3, 3]]

Return matrix representation of the rotation.

scaled_axis(self: lula.Rotation3) → numpy.ndarray[float64[3, 1]]

Return scaled axis represetation of the rotation where magnitude of the returned vector represents the rotation angle in radians.

slerp(rotation0: lula.Rotation3, rotation1: lula.Rotation3, t: float) → lula.Rotation3

Smoothly interpolate between two rotations using spherical linear interpolation (“slerp”).

w(self: lula.Rotation3) → float

Return w component of the quaternion represention of the rotation.

x(self: lula.Rotation3) → float

Return x component of the quaternion represention of the rotation.

y(self: lula.Rotation3) → float

Return y component of the quaternion represention of the rotation.

z(self: lula.Rotation3) → float

Return z component of the quaternion represention of the rotation.

class Pose3

Representation of a pose (i.e. element of SE(3)) in 3D.

from_rotation(rotation: lula::Rotation3) → lula.Pose3

Create a pure rotational pose

from_translation(translation: numpy.ndarray[float64[3, 1]]) → lula.Pose3

Create a pure translational pose.

identity() → lula.Pose3

Create identity pose.

inverse(self: lula.Pose3) → lula.Pose3

Return the inverse pose.

matrix(self: lula.Pose3) → numpy.ndarray[float64[4, 4]]

Return matrix representation of the pose.

property rotation

Rotation component of pose.

property translation

Translation component of pose.

Robot Specification

class RobotDescription

Robot description, consisting of geometric and kinematic properties of a robot.

c_space_coord_name(self: lula.RobotDescription, coord_index: int) → str

Return the name of a given joint of the robot.

default_c_space_configuration(self: lula.RobotDescription) → numpy.ndarray[float64[m, 1]]

Return default joint positions for the robot.

kinematics(self: lula.RobotDescription) → lula.Kinematics

Return the robot kinematics.

num_c_space_coords(self: lula.RobotDescription) → int

Return the number of actuated joints for the robot.

load_robot(robot_description_file: str, robot_urdf: str) → lula.RobotDescription

Load a robot description from a YAML file (robot_description_file) and a URDF (robot_urdf).

load_robot_from_memory(robot_description: str, robot_urdf: str) → lula.RobotDescription

Load a robot description from the contents of a YAML file (robot_description_file) and the contents of a URDF (robot_urdf).

World Specification

class Obstacle

Geometric primitive.

Note

Currently, the CYLINDER obstacle type is internally represented as a capsule (i.e., a cylinder with two hemispherical end caps) extending beyond the nominal HEIGHT. This will be corrected in a future release.

class Attribute

HEIGHT = Attribute.HEIGHT

RADIUS = Attribute.RADIUS

SIDE_LENGTHS = Attribute.SIDE_LENGTHS

class AttributeValue

class Type

CUBE = Type.CUBE

CYLINDER = Type.CYLINDER

SPHERE = Type.SPHERE

set_attribute(self: lula.Obstacle, attribute: lula::Obstacle::Attribute, value: lula::Obstacle::AttributeValue) → None

Set attribute for obstacle

type(self: lula.Obstacle) → lula::Obstacle::Type

Return the type of the obstacle.

create_obstacle(type: lula.Obstacle.Type) → lula.Obstacle

Create an obstacle.

class World

Represents a collection of obstacles.

class ObstacleHandle

add_obstacle(self: lula.World, obstacle: lula.Obstacle, pose: Optional[lula.Pose3] = None) → lula::World::ObstacleHandle

Add obstacle to the world.

add_world_view(self: lula.World) → lula::WorldView

Create a view into the world that can be used for collision checks and distance evaluations.

disable_obstacle(self: lula.World, obstacle: lula::World::ObstacleHandle) → None

Disable an obstacle for the purpose of collision checks and distance evaluations.

enable_obstacle(self: lula.World, obstacle: lula::World::ObstacleHandle) → None

Enable an obstacle for the purpose of collision checks and distance evaluations.

remove_obstacle(self: lula.World, obstacle: lula::World::ObstacleHandle) → None

Permanently remove obstacle, invalidating its handle.

set_pose(self: lula.World, obstacle: lula::World::ObstacleHandle, pose: lula.Pose3) → None

Set the pose of the given obstacle.

create_world() → lula.World

Create a new, empty world.

class WorldView

Represents a view of a lula.World.

distance_to(self: lula.WorldView, obstacle: lula.World.ObstacleHandle, point: numpy.ndarray[float64[3, 1]], gradient: Optional[numpy.ndarray[float64[3, 1], flags.writeable]] = None) → float

Calculate the distance from point to the obstacle specified by obstacle.

distances_to(self: lula.WorldView, point: numpy.ndarray[float64[3, 1]], compute_distance_gradients: bool = True) → Tuple[List[float], Optional[List[numpy.ndarray[float64[3, 1]]]]]

Calculate distances from point to all enabled obstacles.

in_collision(*args, **kwargs)

Overloaded function.

1. in_collision(self: lula.WorldView, center: numpy.ndarray[float64[3, 1]], radius: float) -> bool

Test whether a sphere defined by center and radius is in collision with any enabled obstacles in the world.

2. in_collision(self: lula.WorldView, obstacle: lula.World.ObstacleHandle, center: numpy.ndarray[float64[3, 1]], radius: float) -> bool

Test whether a sphere defined by center and radius is in collision with the obstacle specified by obstacle.

num_enabled_obstacles(self: lula.WorldView) → int

Return the number of enabled obstacles in the current view of the world.

update(self: lula.WorldView) → None

Update WorldView such that any changes to the underlying world are reflected in this view.

Kinematics

class Kinematics

Kinematics interface class.

class Limits

Simple class consisting of upper and lower limits for a given c-space coordinate.

property lower

property upper

base_frame_name(self: lula.Kinematics) → str

Return the name of the base frame of the kinematic structure.

c_space_coord_acceleration_limit(self: lula.Kinematics, coord_index: int) → float

Return the acceleration limit of a given configuration space coordinate of the kinematic structure.

c_space_coord_jerk_limit(self: lula.Kinematics, coord_index: int) → float

Return the jerk limit of a given configuration space coordinate of the kinematic structure.

c_space_coord_limits(self: lula.Kinematics, coord_index: int) → lula.Kinematics.Limits

Return the limits of a given configuration space coordinate of the kinematic structure.

c_space_coord_name(self: lula.Kinematics, coord_index: int) → str

Return the name of a given configuration space coordinate of the kinematic structure.

c_space_coord_velocity_limit(self: lula.Kinematics, coord_index: int) → float

Return the velocity limit of a given configuration space coordinate of the kinematic structure.

frame_names(self: lula.Kinematics) → List[str]

Return all of the frame names in the kinematic structure.

has_c_space_acceleration_limits(self: lula.Kinematics) → bool

Return true if each configuration space coordinate has an associated acceleration limit.

has_c_space_jerk_limits(self: lula.Kinematics) → bool

Return true if each configuration space coordinate has an associated jerk limit.

jacobian(self: lula.Kinematics, cspace_position: numpy.ndarray[float64[m, 1]], frame: str) → numpy.ndarray[float64[6, n]]

Return the Jacobian of the origin of the given frame with respect to the base frame (i.e., base_frame_name()) at the given cspace_position.

The returned Jacobian is a 6 x N matrix where N is the c-space dimension (i.e., num_c_space_coords()). Column i of the returned Jacobian corresponds to the derivative of the origin of frame with respect to the ith c-space coordinate in the coordinates of the base frame. For each column, the first three elements correspond to the translational portion, and the last three elements correspond to the rotational portion.

num_c_space_coords(self: lula.Kinematics) → int

Return the number of configuration space coordinates for the kinematic structure.

orientation(*args, **kwargs)

Overloaded function.

1. orientation(self: lula.Kinematics, cspace_position: numpy.ndarray[float64[m, 1]], frame: str, reference_frame: str) -> lula::Rotation3

Return the orientation of the given frame with respect to reference_frame at the given cspace_position.

2. orientation(self: lula.Kinematics, cspace_position: numpy.ndarray[float64[m, 1]], frame: str) -> lula::Rotation3

Return the orientation of the given frame with respect to the base frame (i.e., base_frame_name()) at the given cspace_position.

orientation_jacobian(self: lula.Kinematics, cspace_position: numpy.ndarray[float64[m, 1]], frame: str) → numpy.ndarray[float64[3, n]]

Return the Jacobian of the orientation of the given frame with respect to the base frame (i.e., base_frame_name()) at the given cspace_position.

The returned Jacobian is a 3 x N matrix where N is the c-space dimension (i.e., num_c_space_coords()). Column i of the returned Jacobian corresponds to the derivative of the orientation of frame with respect to the ith c-space coordinate in the coordinates of the base frame.

pose(*args, **kwargs)

Overloaded function.

1. pose(self: lula.Kinematics, cspace_position: numpy.ndarray[float64[m, 1]], frame: str, reference_frame: str) -> lula::Pose3

Return the pose of the given frame with respect to reference_frame at the given cspace_position.

2. pose(self: lula.Kinematics, cspace_position: numpy.ndarray[float64[m, 1]], frame: str) -> lula::Pose3

Return the pose of the given frame with respect to the base frame (i.e., base_frame_name()) at the given cspace_position.

position(*args, **kwargs)

Overloaded function.

1. position(self: lula.Kinematics, cspace_position: numpy.ndarray[float64[m, 1]], frame: str, reference_frame: str) -> numpy.ndarray[float64[3, 1]]

Return the position of the origin of the given frame with respect to reference_frame at the given cspace_position.

2. position(self: lula.Kinematics, cspace_position: numpy.ndarray[float64[m, 1]], frame: str) -> numpy.ndarray[float64[3, 1]]

Return the position of the origin of the given frame with respect to the base frame (i.e., base_frame_name()) at the given cspace_position.

position_jacobian(self: lula.Kinematics, cspace_position: numpy.ndarray[float64[m, 1]], frame: str) → numpy.ndarray[float64[3, n]]

Return the Jacobian of the position of the origin of the given frame with respect to the base frame (i.e., base_frame_name()) at the given cspace_position.

The returned Jacobian is a 3 x N matrix where N is the c-space dimension (i.e., num_c_space_coords()). Column i of the returned Jacobian corresponds to the derivative of the position of the origin of frame with respect to the ith c-space coordinate in the coordinates of the base frame.

within_cspace_limits(self: lula.Kinematics, cspace_position: numpy.ndarray[float64[m, 1]], log_warnings: bool) → bool

Determine whether a specified configuration space position is within limits.

Inverse Kinematics

class CyclicCoordDescentIkConfig

Configuration parameters for CCD inverse kinematics solver.

property cspace_seeds

Optional parameter to set the initial c-space configurations for descent.

property descent_termination_delta

Minimal change in c-space coordinates for early descent termination.

property irwin_hall_sampling_order

Sampling distribution for initial c-space positions.

property max_iterations_per_descent

Number of iterations used for each cyclic coordinate descent.

property max_num_descents

Maximum number of c-space positions that will be used as seeds.

property orientation_tolerance

Maximum orientation error (per-axis L2-norm) for a successful IK solution

property orientation_weight

Weight for the relative importance of position error during CCD

property position_tolerance

Maximum position error (L2-norm) for a successful IK solution

property position_weight

Weight for the relative importance of position error during CCD

property sampling_seed

Seed for Irwin-Hall sampling of initial c-space positions

class CyclicCoordDescentIkResults

Results returned by CCD inverse kinematics solver.

property cspace_position

If success is true, joint configuration corresponding to target_pose.

property num_descents

Number of unique c-sapce positions used for CCD prior to termination.

property position_error

Position error (L2-norm) of returned c-space position

property success

Indicate whether a cspace_position within the tolerances has been found.

property x_axis_orientation_error

X-axis orientation error (L2-norm) of returned c-space position

property y_axis_orientation_error

Y-axis orientation error (L2-norm) of returned c-space position

property z_axis_orientation_error

Z-axis orientation error (L2-norm) of returned c-space position

compute_ik_ccd(kinematics: lula::Kinematics, target_pose: lula::Pose3, target_frame: str, config: lula.CyclicCoordDescentIkConfig) → lula.CyclicCoordDescentIkResults

Attempt to solve inverse kinematics using cyclic coordinate descent.

Path Specification

class CSpacePathSpec

Procedurally specify a CSpacePathSpec from a series of configuration space waypoints

add_c_space_waypoint(self: lula.CSpacePathSpec, waypoint: numpy.ndarray[float64[m, 1]]) → bool

Add a path to connect the previous configuration to the waypoint.

num_c_space_coords(self: lula.CSpacePathSpec) → int

Return the number of configuration space coordinates for the path specification.

create_c_space_path_spec(initial_c_space_position: numpy.ndarray[float64[m, 1]]) → lula.CSpacePathSpec

Create a ‘CSpacePathSpec’ with the specified ‘initial_c_space_position’.

class TaskSpacePathSpec

Procedurally compose a TaskSpacePathSpec from a series of continuous task space segments

add_linear_path(self: lula.TaskSpacePathSpec, target_pose: lula.Pose3, blend_radius: float = 0.0) → bool

Add a path to linearly connect the previous pose to the ‘target_pose’.

add_rotation(self: lula.TaskSpacePathSpec, target_rotation: lula.Rotation3) → bool

Add a rotation-only path connecting the previous pose to the target_rotation.

add_tangent_arc(self: lula.TaskSpacePathSpec, target_position: numpy.ndarray[float64[3, 1]], constant_orientation: bool = True) → bool

Add a path to connect the previous pose to the ‘target_position’ along a circular arc that is tangent to the previous segment.

add_tangent_arc_with_orientation_target(self: lula.TaskSpacePathSpec, target_pose: lula.Pose3) → bool

Add a path to connect the previous pose to the ‘target_pose’ along a circular arc that is tangent to the previous segment.

add_three_point_arc(self: lula.TaskSpacePathSpec, target_position: numpy.ndarray[float64[3, 1]], intermediate_position: numpy.ndarray[float64[3, 1]], constant_orientation: bool = True) → bool

Add a path to connect the previous pose to the ‘target_position’ along a circular arc that passes through ‘intermediate_position’.

add_three_point_arc_with_orientation_target(self: lula.TaskSpacePathSpec, target_pose: lula.Pose3, intermediate_position: numpy.ndarray[float64[3, 1]]) → bool

Add a path to connect the previous pose to the ‘target_pose’ along a circular arc that passes through ‘intermediate_position’.

add_translation(self: lula.TaskSpacePathSpec, target_position: numpy.ndarray[float64[3, 1]], blend_radius: float = 0.0) → bool

Add a translation-only path to linearly connect the previous pose to the ‘target_position’

generate_path(self: lula.TaskSpacePathSpec) → lula.TaskSpacePath

Generate a continuous path between all of the procedurally added task space path segments.

create_task_space_path_spec(initial_pose: lula.Pose3) → lula.TaskSpacePathSpec

Create a ‘TaskSpacePathSpec’ with the specified ‘initial_pose’.

class CompositePathSpec

Procedurally compose ‘CSpacePathSpec’ and ‘TaskSpacePathSpec’ segments into a single path specification.

class PathSpecType

CSPACE = PathSpecType.CSPACE

TASK_SPACE = PathSpecType.TASK_SPACE

class TransitionMode

FREE = TransitionMode.FREE

LINEAR_TASK_SPACE = TransitionMode.LINEAR_TASK_SPACE

SKIP = TransitionMode.SKIP

add_c_space_path_spec(self: lula.CompositePathSpec, path_spec: lula.CSpacePathSpec, transition_mode: lula.CompositePathSpec.TransitionMode) → bool

Add a c-space ‘path_spec’ to the ‘CompositePathSpec’ with the specified ‘transition_mode’.

add_task_space_path_spec(self: lula.CompositePathSpec, path_spec: lula::TaskSpacePathSpec, transition_mode: lula.CompositePathSpec.TransitionMode) → bool

Add a task space ‘path_spec’ to the ‘CompositePathSpec’ with the specified ‘transition_mode’.

c_space_path_spec(self: lula.CompositePathSpec, path_spec_index: int) → lula.CSpacePathSpec

Return the ‘CSpacePathSpec’ at the given ‘path_spec_index’.

num_c_space_coords(self: lula.CompositePathSpec) → int

Return the number of configuration space coordinates for the path specification.

num_path_specs(self: lula.CompositePathSpec) → int

Return the number of path specifications contained in the ‘CompositePathSpec’.

path_spec_type(self: lula.CompositePathSpec, path_spec_index: int) → lula.CompositePathSpec.PathSpecType

Given a ‘path_spec_index’ in range [0, ‘num_path_specs()’), return the type of the corresponding path specification.

task_space_path_spec(self: lula.CompositePathSpec, path_spec_index: int) → lula::TaskSpacePathSpec

Return the ‘TaskSpacePathSpec’ at the given ‘path_spec_index’.

create_composite_path_spec(initial_c_space_position: numpy.ndarray[float64[m, 1]]) → lula.CompositePathSpec

Create a ‘CompositePathSpec’ with the specified ‘initial_c_space_position’.

load_c_space_path_spec_from_file(c_space_path_spec_file: str) → lula.CSpacePathSpec

Load a ‘CSpacePathSpec’ from file with absolute path ‘c_space_path_spec_file’.

load_c_space_path_spec_from_memory(c_space_path_spec_yaml: str) → lula.CSpacePathSpec

Load a ‘CSpacePathSpec’ from the contents of a YAML file (‘c_space_path_spec_yaml’).

export_c_space_path_spec_to_memory(c_space_path_spec: lula.CSpacePathSpec) → str

Export ‘c_space_path_spec’ as a string.

load_task_space_path_spec_from_file(task_space_path_spec_file: str) → lula::TaskSpacePathSpec

Load a ‘TaskSpacePathSpec’ from file with absolute path ‘task_space_path_spec_file’.

load_task_space_path_spec_from_memory(task_space_path_spec_yaml: str) → lula::TaskSpacePathSpec

Load a ‘TaskSpacePathSpec’ from the contents of a YAML file (‘task_space_path_spec_yaml’).

export_task_space_path_spec_to_memory(task_space_path_spec: lula::TaskSpacePathSpec) → str

Export ‘task_space_path_spec’ as a string.

load_composite_path_spec_from_file(composite_path_spec_file: str) → lula.CompositePathSpec

Load a ‘CompositePathSpec’ from file with absolute path ‘composite_path_spec_file’.

load_composite_path_spec_from_memory(composite_path_spec_yaml: str) → lula.CompositePathSpec

Load a ‘CompositePathSpec’ from the contents of a YAML file (‘composite_path_spec_yaml’).

export_composite_path_spec_to_memory(composite_path_spec: lula.CompositePathSpec) → str

Export ‘composite_path_spec’ as a string.

Path Generation

class CSpacePath

Represent a path through configuration space (i.e., c-space or “joint space”).

class Domain

Indicates the continuous range of independent values, ‘s’, for which the path is defined.

property lower

span(self: lula.CSpacePath.Domain) → float

Convenience function to return the span of ‘s’ values included in domain.

property upper

domain(self: lula.CSpacePath) → lula.CSpacePath.Domain

Return the domain for the path.

eval(self: lula.CSpacePath, s: float) → numpy.ndarray[float64[m, 1]]

Evaluate the path at the given ‘s’.

max_position(self: lula.CSpacePath) → numpy.ndarray[float64[m, 1]]

Return the maximum x, y, and z positions reached by the path (not necessarily simultaneously) within the defined ‘domain()’.

min_position(self: lula.CSpacePath) → numpy.ndarray[float64[m, 1]]

Return the minimum x, y, and z positions reached by the path (not necessarily simultaneously) within the defined ‘domain()’.

num_c_space_coords(self: lula.CSpacePath) → int

Return the number of configuration space coordinates for the path.

path_length(self: lula.CSpacePath) → float

Return the total translation distance accumulated along the path, where distance is computed using the L2-norm.

class LinearCSpacePath

Represent a path linearly interpolated through configuration space (i.e., c-space) waypoints.

domain(self: lula.LinearCSpacePath) → lula.CSpacePath.Domain

Return the domain for the path.

eval(self: lula.LinearCSpacePath, s: float) → numpy.ndarray[float64[m, 1]]

Evaluate the path at the given ‘s’.

max_position(self: lula.LinearCSpacePath) → numpy.ndarray[float64[m, 1]]

Return the maximum x, y, and z positions reached by the path (not necessarily simultaneously) within the defined ‘domain()’.

min_position(self: lula.LinearCSpacePath) → numpy.ndarray[float64[m, 1]]

Return the minimum x, y, and z positions reached by the path (not necessarily simultaneously) within the defined ‘domain()’.

num_c_space_coords(self: lula.LinearCSpacePath) → int

Return the number of configuration space coordinates for the path.

path_length(self: lula.LinearCSpacePath) → float

Return the total translation distance accumulated along the path, where distance is computed using the L2-norm.

waypoints(self: lula.LinearCSpacePath) → List[numpy.ndarray[float64[m, 1]]]

Return all of the waypoints through which the path is linearly interpolated (including the initial and final c-space configurations).

create_linear_c_space_path(c_space_path_spec: lula.CSpacePathSpec) → lula.LinearCSpacePath

Create a ‘LinearCSpacePath’ from a c-space path specification.

class TaskSpacePath

Represent a path through task space (i.e., SE(3) group representing 6-dof poses).

class Domain

Indicates the continuous range of independent values, ‘s’, for which the path is defined.

property lower

span(self: lula.TaskSpacePath.Domain) → float

Convenience function to return the span of ‘s’ values included in domain.

property upper

accumulated_rotation(self: lula.TaskSpacePath) → float

Return the total angular distance (in radians) accumulated throughout the path.

domain(self: lula.TaskSpacePath) → lula.TaskSpacePath.Domain

Return the domain for the path.

eval(self: lula.TaskSpacePath, s: float) → lula.Pose3

Evaluate the path at the given ‘s’.

max_position(self: lula.TaskSpacePath) → numpy.ndarray[float64[3, 1]]

Return the maximum x, y, and z positions reached by the path (not necessarily simultaneously) within the defined ‘domain()’.

min_position(self: lula.TaskSpacePath) → numpy.ndarray[float64[3, 1]]

Return the minimum x, y, and z positions reached by the path (not necessarily simultaneously) within the defined ‘domain()’.

path_length(self: lula.TaskSpacePath) → float

Return the total translation distance accumulated along the path.

class TaskSpacePathConversionConfig

Configuration parameters for converting a ‘TaskSpacePathSpec’ into a series of c-space configurations.

property alpha

“alpha” is used to exponentially scale the ‘s’ step size “delta” to speed convergence when the ‘s’ step size is being successively increased or successively decreased. When an increase is followed by a decrease, or vice versa, “alpha” is used to decrease the ‘s’ step size “delta” to reduce overshoot. The default value is generally recommended. ‘alpha’ must be greater than 1. Default value is 1.4.

property initial_s_step_size

Initial step size in the domain value ‘s’ used to sample poses from the task space path to be converted to c-space waypoints. The ‘s’ step size will be adaptively updated throughout the path conversion and the default value for initialization is generally recommended. ‘initial_s_step_size’ must be positive. Default value is 0.05.

property initial_s_step_size_delta

Initial step size “delta” that is used to adaptively adjust the ‘s’ step size; ‘s’ is the domain value ‘s’ used to sample poses from the task space path to be converted to c-space waypoints. The ‘s’ step size “delta” will be adaptively updated throughout the path conversion and the default value for initialization is generally recommended. ‘initial_s_step_size_delta’ must be positive. Default value is 0.005.

property max_iterations

Maximum number of iterations to search for each c-space waypoint. If ‘max_iterations’ is reached for any c-space waypoint, then path conversion will fail. ‘max_iterations’ must be positive. Default value is 50.

property max_position_deviation

For each c-space waypoint that is generated, the position deviation between the desired task space path and a task space mapping of a straight-line interpolation in c-space is approximated. The maximum position deviation places an upper bound of deviation allowed to add a c-space waypoint. ‘max_position_deviation’ must be positive and greater than ‘min_position_deviation’. Default value is 0.003.

property min_position_deviation

For each c-space waypoint that is generated, the position deviation between the desired task space path and a task space mapping of a straight-line interpolation in c-space is approximated. The minimum position deviation places a lower bound of deviation required to add a c-space waypoint. While it is somewhat unintuitive that the deviation could be too small, this minimum deviation is used to control the minimum spacing between c-space configurations along the task space path domain. A (relatively) sparse series of c-space waypoints is desirable for trajectory generation; if the minimum deviation is arbitrarily small then the c-space points will be (in general) too close together to generate a time-optimal trajectory. Generation of excessive c-space waypoints will also be computationally expensive and is, in general, best avoided. ‘min_position_deviation’ must be positive and less than ‘max_position_deviation’. Default value is 0.001.

property min_s_step_size

Minimum allowable interval in domain value ‘s’ that can separate poses from the task space path to be converted to c-space waypoints. The minimum ‘s’ step size serves to limit the number of c-space configurations that can be returned in the converted path. Specifically, the upper bound for the number of returned c-space configurations is (“span of the task space path domain” / min_s_step_size) + 1. ‘min_s_step_size’ must be positive. Default value is 1e-5.

property min_s_step_size_delta

Minimum allowable ‘s’ step size “delta” used to adaptively update the ‘s’ step size. The ‘min_s_step_size_delta’ serves to limit wasted iterations when (minimal) progress is being made towards path conversion. If ‘min_s_step_size_delta’ is reached during the search for any c-space waypoint, then path conversion will fail. The default value is generally recommended. ‘min_s_step_size_delta` must be positive’. Default value is 1e-5.

convert_composite_path_spec_to_c_space(composite_path_spec: lula.CompositePathSpec, kinematics: lula.Kinematics, control_frame: str, task_space_path_conversion_config: lula.TaskSpacePathConversionConfig=<lula.TaskSpacePathConversionConfig object at 0x7f991adfabf0>, ik_config: lula.CyclicCoordDescentIkConfig=<lula.CyclicCoordDescentIkConfig object at 0x7f991adfabb0>) → lula.LinearCSpacePath

Convert a composite_path_spec into a linear c-space path.

convert_task_space_path_spec_to_c_space(task_space_path_spec: lula::TaskSpacePathSpec, kinematics: lula.Kinematics, control_frame: str, task_space_path_conversion_config: lula.TaskSpacePathConversionConfig=<lula.TaskSpacePathConversionConfig object at 0x7f991adfacf0>, ik_config: lula.CyclicCoordDescentIkConfig=<lula.CyclicCoordDescentIkConfig object at 0x7f991adfa970>) → lula.LinearCSpacePath

Convert a task_space_path_spec into a linear c-space path.

Trajectory Generation

class Trajectory

Represent a path through configuration space (i.e., “c-space”) parameterized by time.

class Domain

Indicates the continuous range of time values, ‘t’, for which the trajectory and its derivatives are defined.

property lower

span(self: lula.Trajectory.Domain) → float

Convenience function to return the span of time values included in domain.

property upper

domain(self: lula.Trajectory) → lula.Trajectory.Domain

Return the domain for the trajectory.

eval(self: lula.Trajectory, time: float, derivative_order: int = 0) → numpy.ndarray[float64[m, 1]]

Evaluate specified trajectory derivative at the given ‘time’ and return value.

eval_all(self: lula.Trajectory, arg0: float) → Tuple[numpy.ndarray[float64[m, 1]], numpy.ndarray[float64[m, 1]], numpy.ndarray[float64[m, 1]], numpy.ndarray[float64[m, 1]]]

Evaluate the trajectory at the given ‘time’, returning position, velocity, acceleration, and jerk.

max_acceleration_magnitude(self: lula.Trajectory) → numpy.ndarray[float64[m, 1]]

Return the maximum magnitude of acceleration for each c-space coordinate within the defined ‘domain()’.

max_jerk_magnitude(self: lula.Trajectory) → numpy.ndarray[float64[m, 1]]

Return the maximum magnitude of jerk for each c-space coordinate within the defined ‘domain()’.

max_position(self: lula.Trajectory) → numpy.ndarray[float64[m, 1]]

Return the maximum position for each c-space coordinate within the defined ‘domain()’.

max_velocity_magnitude(self: lula.Trajectory) → numpy.ndarray[float64[m, 1]]

Return the maximum magnitude of velocity for each c-space coordinate within the defined ‘domain()’.

min_position(self: lula.Trajectory) → numpy.ndarray[float64[m, 1]]

Return the minimum position for each c-space coordinate within the defined ‘domain()’.

num_c_space_coords(self: lula.Trajectory) → int

Return the number of configuration space coordinates for the trajectory.

class CSpaceTrajectoryGenerator

Configure a trajectory generator that can compute smooth trajectories.

class SolverParamValue

Value for a given parameter.

generate_trajectory(self: lula.CSpaceTrajectoryGenerator, waypoints: List[numpy.ndarray[float64[m, 1]]]) → lula.Trajectory

Attempt to generate a trajectory with the specified constraints.

num_c_space_coords(self: lula.CSpaceTrajectoryGenerator) → int

Return the number of configuration space coordinates for the trajectory generator

set_acceleration_limits(self: lula.CSpaceTrajectoryGenerator, max_acceleration: numpy.ndarray[float64[m, 1]]) → None

Set acceleration limits.

set_jerk_limits(self: lula.CSpaceTrajectoryGenerator, max_jerk: numpy.ndarray[float64[m, 1]]) → None

Set jerk limits.

set_position_limits(self: lula.CSpaceTrajectoryGenerator, min_position: numpy.ndarray[float64[m, 1]], max_position: numpy.ndarray[float64[m, 1]]) → None

Set position limits.

set_solver_param(self: lula.CSpaceTrajectoryGenerator, param_name: str, value: lula.CSpaceTrajectoryGenerator.SolverParamValue) → bool

Set the value of the solver parameter.

set_velocity_limits(self: lula.CSpaceTrajectoryGenerator, max_velocity: numpy.ndarray[float64[m, 1]]) → None

Set velocity limits.

create_c_space_trajectory_generator(*args, **kwargs)

Overloaded function.

1. create_c_space_trajectory_generator(num_c_space_coords: int) -> lula.CSpaceTrajectoryGenerator

Create a CreateCSpaceTrajectoryGenerator with the specified number of configuration space coordinates.

2. create_c_space_trajectory_generator(kinematics: lula.Kinematics) -> lula.CSpaceTrajectoryGenerator

Create a CreateCSpaceTrajectoryGenerator with the specified ‘kinematics’.

Collision Sphere Generation

class CollisionSphereGenerator

Configure a generator that can generate spheres to approximate mesh volumes.

class ParamValue

Value for a given parameter.

class Sphere

Simple representation of a sphere.

property center

property radius

generate_spheres(self: lula.CollisionSphereGenerator, num_spheres: int, radius_offset: float) → List[lula.CollisionSphereGenerator.Sphere]

Generate a set of num_spheres that approximate the volume of the specified mesh

get_sampled_spheres(self: lula.CollisionSphereGenerator) → List[lula.CollisionSphereGenerator.Sphere]

Return all of the medial axis spheres used to approximate the volume of the mesh. The spheres returned by generateSpheres() are selected from this set.

num_triangles(self: lula.CollisionSphereGenerator) → int

Return the number of validated triangles that have been included in the mesh used for sampling spheres to approximate volume.

set_param(self: lula.CollisionSphereGenerator, param_name: str, value: lula.CollisionSphereGenerator.ParamValue) → bool

Set the value of the parameter.

create_collision_sphere_generator(vertices: List[numpy.ndarray[float64[3, 1]]], triangles: List[numpy.ndarray[int32[3, 1]]]) → lula.CollisionSphereGenerator

Create a CollisionSphereGenerator to generate spheres that approximate the volume of a mesh represented by vertices and triangles.

Motion Planning

class MotionPlanner

Interface for planning collision-free paths for robotic manipulators.

class Limit

Simple class consisting of upper and lower limits for a variable.

property lower

property upper

class ParamValue

Value for a given parameter.

class Results

Results from a path search.

property interpolated_path

property path

property path_found

plan_to_cspace_target(self: lula.MotionPlanner, q_initial: numpy.ndarray[float64[m, 1]], q_target: numpy.ndarray[float64[m, 1]], generate_interpolated_path: bool = False) → lula::MotionPlanner::Results

Attempt to find path to configuration space target

plan_to_task_space_target(self: lula.MotionPlanner, q_initial: numpy.ndarray[float64[m, 1]], x_target: numpy.ndarray[float64[3, 1]], generate_interpolated_path: bool = False) → lula::MotionPlanner::Results

Attempt to find path to task space target

set_param(*args, **kwargs)

Overloaded function.

1. set_param(self: lula.MotionPlanner, param_name: str, value: numpy.ndarray[float64[3, 1]]) -> bool

Set parameter for motion planner.

2. set_param(self: lula.MotionPlanner, param_name: str, value: List[float]) -> bool

Set parameter for motion planner.

3. set_param(self: lula.MotionPlanner, param_name: str, value: List[lula::MotionPlanner::Limit]) -> bool

Set parameter for motion planner.

4. set_param(self: lula.MotionPlanner, param_name: str, value: lula::MotionPlanner::ParamValue) -> bool

Set parameter for motion planner.

update_world_view(self: lula.MotionPlanner) → None

Update the internal WorldView to latest state of its underlying World.

create_motion_planner(*args, **kwargs)

Overloaded function.

1. create_motion_planner(planning_config_file: str, robot_description: lula::RobotDescription, world_view: lula::WorldView) -> lula.MotionPlanner

Create an MotionPlanner interface from configuration parameters, robot description and world view.

2. create_motion_planner(robot_description: lula::RobotDescription, world_view: lula::WorldView) -> lula.MotionPlanner

Create an MotionPlanner interface from robot description and world view, using default configuration parameters.

RMPflow

class RmpFlowConfig

RMPflow configuration, including parameters and robot description.

get_all_params(self: lula.RmpFlowConfig, names: List[str], values: List[float]) → None

Get the names and values of all parameters.

The two lists will be overwritten if not empty.

Parameters

• names (List[str]) – List of all parameter names.

• values (List[float]) – Values of all parameters, in same order as names.

Returns

None

get_param(self: lula.RmpFlowConfig, param_name: str) → float

Get the value of an RMPflow parameter.

Parameters

param_name (str) – Fully-qualified parameter name of the form <rmp_name>/<parameter_name>.

Returns

Current value of the parameter.

Return type

float

set_all_params(self: lula.RmpFlowConfig, names: List[str], values: List[float]) → None

Set all parameters at once.

The lists names and values must have the same size. The parameter corresponding to names[i] will be set to the value given by values[i].

Parameters

• names (List[str]) – List of all parameter names.

• values (List[float]) – Desired values for all parameters, in same order as names.

Returns

None

set_param(self: lula.RmpFlowConfig, param_name: str, value: float) → None

Set the value of an RMPflow parameter.

Parameters

• param_name (str) – Fully-qualified parameter name of the form <rmp_name>/<parameter_name>.

• value (float) – New value for the parameter.

Returns

None

set_world_view(self: lula.RmpFlowConfig, world_view: lula::WorldView) → None

Set the world view that will be used for obstacle avoidance.

All enabled obstacles in world_view will be avoided by the RMPflow policy.

Parameters

world_view (lula.WorldView) – Input world view.

Returns

None

create_rmpflow_config(rmpflow_config_file: str, robot_description: lula::RobotDescription, end_effector_frame: str, world_view: lula::WorldView) → lula.RmpFlowConfig

Create an RMPflow configuration object.

This function loads a set of RMPflow parameters from a file and combines them with a robot description to create a configuration object for consumption by lula.create_rmpflow().

Parameters

• rmpflow_config_file (str) – Path to RMPflow configuration file.

• robot_description (lula.RobotDescription) – RobotDescription object, e.g. created by lula.load_robot().

• end_effector_frame (str) – This control frame name must correspond to a link name as specified in the original URDF used to create the robot description.

• world_view (lula.WorldView) – World view that will be used for obstacle avoidance.

Returns

RMPflow motion policy interface object.

Return type

lula.RmpFlow

create_rmpflow_config_from_memory(rmpflow_config: str, robot_description: lula::RobotDescription, end_effector_frame: str, world_view: lula::WorldView) → lula.RmpFlowConfig

Parameters

• rmpflow_config (str) – RMPflow configuration as a single string (unparsed YAML).

• robot_description (lula.RobotDescription) – RobotDescription object, e.g. created by lula.load_robot().

• end_effector_frame (str) – This control frame name must correspond to a link name as specified in the original URDF used to create the robot description.

• world_view (lula.WorldView) – World view that will be used for obstacle avoidance.

Returns

RMPflow motion policy interface object.

Return type

lula.RmpFlow

class RmpFlow

Interface for building and evaluating an RMPflow motion policy.

clear_end_effector_orientation_attractor(self: lula.RmpFlow) → None

Clear end-effector orientation attractor.

clear_end_effector_position_attractor(self: lula.RmpFlow) → None

Clear end-effector position attractor.

collision_sphere_positions(self: lula.RmpFlow, cspace_position: numpy.ndarray[float64[m, 1]]) → List[numpy.ndarray[float64[3, 1]]]

Compute positions of all collision spheres on the robot at the specified cspace_position

collision_sphere_radii(self: lula.RmpFlow) → List[float]

Return the radii of each collision sphere on the robot.

distance_to_obstacle(self: lula.RmpFlow, obstacle: lula::World::ObstacleHandle, collision_sphere_index: int, cspace_position: numpy.ndarray[float64[m, 1]]) → float

Compute the distance between a given obstacle and collision sphere for the provided position in configuration space.

eval_accel(self: lula.RmpFlow, cspace_position: numpy.ndarray[float64[m, 1]], cspace_velocity: numpy.ndarray[float64[m, 1]], cspace_accel: numpy.ndarray[float64[m, 1], flags.writeable]) → None

Compute configuration-space acceleration from motion policy, given input state.

eval_force_and_metric(self: lula.RmpFlow, cspace_position: numpy.ndarray[float64[m, 1]], cspace_velocity: numpy.ndarray[float64[m, 1]]) → Tuple[numpy.ndarray[float64[m, 1]], numpy.ndarray[float64[m, n]]]

Compute configuration-space force and metric from motion policy, given input state.

in_collision_with_obstacle(self: lula.RmpFlow, cspace_position: numpy.ndarray[float64[m, 1]]) → bool

Determine whether a specified joint configuration puts the robot into collision with an obstacle.

num_collision_spheres(self: lula.RmpFlow) → int

Return the number of collision spheres in the robot representation.

set_cspace_attractor(self: lula.RmpFlow, cspace_position: numpy.ndarray[float64[m, 1]]) → None

Set an attractor in generalized coordinates (configuration space).

set_cspace_target(self: lula.RmpFlow, cspace_target: numpy.ndarray[float64[m, 1]]) → None

Set a target in generalized coordinates (configuration space).

Warning

This function is part of a legacy interface for setting targets that is deprecated and slated for removal in a future release. It is recommended that this function not be used.

set_end_effector_orientation_attractor(self: lula.RmpFlow, orientation: lula::Rotation3) → None

Set an end-effector orientation attractor.

set_end_effector_position_attractor(self: lula.RmpFlow, position: numpy.ndarray[float64[3, 1]]) → None

Set an end-effector position attractor.

set_end_effector_target(self: lula.RmpFlow, position: Optional[numpy.ndarray[float64[3, 1]]]=None, orientation: Optional[lula::Rotation3]=None, default_cspace_config: Optional[numpy.ndarray[float64[m, 1]]]=None) → None

Set an end-effector target pose, along with a default configuration for the robot.

Warning

This function is part of a legacy interface for setting targets that is deprecated and slated for removal in a future release. It is recommended that this function not be used.

update_end_effector_target(self: lula.RmpFlow, position: Optional[numpy.ndarray[float64[3, 1]]]=None, orientation: Optional[lula::Rotation3]=None, default_cspace_config: Optional[numpy.ndarray[float64[m, 1]]]=None) → None

Update end-effector target pose and default configuration.

Warning

This function is part of a legacy interface for setting targets that is deprecated and slated for removal in a future release. It is recommended that this function not be used.

update_world_view(self: lula.RmpFlow) → None

Update the internal WorldView to latest state of its underlying World.

create_rmpflow(config: lula.RmpFlowConfig) → lula.RmpFlow

Create an instance of the RmpFlow interface from an RMPflow configuration.

Geometric Fabrics

Note

Lula’s support for motion policies based on geometric fabrics is under active development and will be exposed in a future release.