diff --git a/examples/kinematics/README.md b/examples/kinematics/README.md new file mode 100644 index 0000000..6a7dcfd --- /dev/null +++ b/examples/kinematics/README.md @@ -0,0 +1,7 @@ +## Robot kinematics + +We provide examples on how to perform forward and inverse kinematics. + +References: +[1] "Robotics: Modelling, Planning and Control", Siciliano et al., 2010 +[2] "Springer Handbook of Robotics", Siciliano et al., 2008 diff --git a/examples/kinematics/forward/data.txt b/examples/kinematics/forward/data.txt new file mode 100644 index 0000000..7dbbd7b --- /dev/null +++ b/examples/kinematics/forward/data.txt @@ -0,0 +1,5138 @@ +(lp0 +(lp1 +F8.8430527e-05 +aF0.0711378917 +aF-0.000168059886 +aF-0.971690439 +aF1.6830881e-05 +aF0.371467111 +aF5.62890805e-05 +aa(lp2 +F8.91636576231491e-05 +aF0.07114374079546631 +aF-0.00016882993920675898 +aF-0.9716886529835815 +aF1.6895725142441245e-05 +aF0.37146589917864514 +aF5.632762668456705e-05 +aa(lp3 +F4.431433394448099e-05 +aF0.07114916965002786 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a/examples/kinematics/forward/fk.py b/examples/kinematics/forward/fk.py new file mode 100644 index 0000000..fa813c0 --- /dev/null +++ b/examples/kinematics/forward/fk.py @@ -0,0 +1,56 @@ +#!/usr/bin/env python +"""In this file, we perform forward kinematics using the Kuka robot. + +The Kuka robot just draw a circle in the air. The joint positions are in the `data.txt` file. +""" + +import os +import pickle +from itertools import count + +from pyrobolearn.simulators import Bullet +from pyrobolearn.worlds import BasicWorld +from pyrobolearn.robots import KukaIIWA, Body + + +# Create simulator +sim = Bullet() + +# create world +world = BasicWorld(sim) + +# create robot +robot = KukaIIWA(sim) +robot.print_info() + +# define useful variables for FK +link_id = robot.get_end_effector_ids(end_effector=0) +joint_ids = robot.joints # actuated joint + +# load data +with open(os.path.dirname(os.path.abspath(__file__)) + '/data.txt', 'rb') as f: + positions = pickle.load(f) + +# set initial joint position +robot.reset_joint_states(q=positions[0]) + +# draw a sphere at the position of the end-effector +sphere = world.load_visual_sphere(position=robot.get_link_world_positions(link_id), + radius=0.05, color=(1, 0, 0, 0.5)) +sphere = Body(sim, body_id=sphere) + +# perform simulation +for t in count(): + + # if no more joint positions, get out of the loop + if t > len(positions): + break + + # set joint positions + robot.set_joint_positions(positions[t], joint_ids=joint_ids) + + # make the sphere follow the end effector + sphere.position = robot.get_link_world_positions(link_id) + + # step in simulation + world.step(sleep_dt=1./240) diff --git a/examples/kinematics/inverse/ik.py b/examples/kinematics/inverse/ik.py new file mode 100644 index 0000000..6f0f28a --- /dev/null +++ b/examples/kinematics/inverse/ik.py @@ -0,0 +1,106 @@ +#!/usr/bin/env python +"""In this file, we perform inverse kinematics using the Kuka robot. + +Set the `solver_flag` to a number between 0 and 1 (see lines [19,22]) to select which IK solver to select. +0: use robot.calculate_inverse_kinematics() +1: use damped-least-squares IK using Jacobian (provided by pybullet) +""" + +import numpy as np +from itertools import count + +from pyrobolearn.simulators import Bullet +from pyrobolearn.worlds import BasicWorld +from pyrobolearn.robots import KukaIIWA + + +# select IK solver, by setting the flag: +# 0 = pybullet + calculate_inverse_kinematics() +# 1 = pybullet + damped-least-squares IK using Jacobian (provided by pybullet) +solver_flag = 1 # 1 and 4 gives pretty good results + + +# Create simulator +sim = Bullet() + +# create world +world = BasicWorld(sim) + +# create robot +robot = KukaIIWA(sim) +robot.print_info() + +# define useful variables for IK +dt = 1./240 +link_id = robot.get_end_effector_ids(end_effector=0) +joint_ids = robot.joints # actuated joint +damping = 0.01 # for damped-least-squares IK +wrt_link_id = -1 # robot.get_link_ids('iiwa_link_1') + +# desired position +xd = np.array([0.5, 0., 0.5]) +world.load_visual_sphere(xd, radius=0.05, color=(1, 0, 0, 0.5)) + +# joint_ids = joint_ids[2:] + +robot.change_transparency() +robot.draw_link_frames([-1, 0]) +robot.draw_bounding_boxes(joint_ids[0]) +# robot.draw_link_coms([-1,0]) + +qIdx = robot.get_q_indices(joint_ids) + + +# OPTION 1: using `calculate_inverse_kinematics`### +if solver_flag == 0: + for _ in count(): + # get current position in the task/operational space + x = robot.get_link_world_positions(link_id) + # print("(xd - x) = {}".format(xd - x)) + + # perform full IK + q = robot.calculate_inverse_kinematics(link_id, position=xd) + + # set the joint positions + robot.set_joint_positions(q[qIdx], joint_ids) + + # step in simulation + world.step(sleep_dt=dt) + +# OPTION 2: using Jacobian and manual damped-least-squares IK ### +elif solver_flag == 1: + kp = 50 # 5 if velocity control, 50 if position control + kd = 0 # 2*np.sqrt(kp) + + for _ in count(): + # get current position in the task/operational space + x = robot.get_link_world_positions(link_id) + dx = robot.get_link_world_linear_velocities(link_id) + # print("(xd - x) = {}".format(xd - x)) + + # Get joint configuration + q = robot.get_joint_positions() + + # Get linear jacobian + if robot.has_floating_base(): + J = robot.get_linear_jacobian(link_id, q=q)[:, qIdx + 6] + else: + J = robot.get_linear_jacobian(link_id, q=q)[:, qIdx] + + # Pseudo-inverse + # Jp = robot.get_pinv_jacobian(J) + # Jp = J.T.dot(np.linalg.inv(J.dot(J.T) + damping*np.identity(3))) # this also works + Jp = robot.get_damped_least_squares_inverse(J, damping) + + # evaluate damped-least-squares IK + dq = Jp.dot(kp * (xd - x) - kd * dx) + + # set joint velocities + # robot.set_joint_velocities(dq) + + # set joint positions + q = q[qIdx] + dq * dt + robot.set_joint_positions(q, joint_ids=joint_ids) + + # step in simulation + world.step(sleep_dt=dt) diff --git a/examples/kinematics/inverse/ik_libraries.py b/examples/kinematics/inverse/ik_libraries.py new file mode 100644 index 0000000..7839b30 --- /dev/null +++ b/examples/kinematics/inverse/ik_libraries.py @@ -0,0 +1,318 @@ +#!/usr/bin/env python +"""In this file, we use and compare several IK libraries using the Kuka robot. + +Namely, we compare: pybullet, PyKDL, trac_ik, and rbdl. + +Set the `solver_flag` to a number between 0 and 4 (see lines [53,60]) to select which solver to select. +0 = pybullet + calculate_inverse_kinematics() +1 = pybullet + damped-least-squares IK using Jacobian (provided by pybullet) +2 = PyKDL +3 = trac_ik +4 = rbdl + damped-least-squares IK using Jacobian (provided by rbdl) +""" + +import os +import numpy as np +from itertools import count + +from pyrobolearn.simulators import Bullet +from pyrobolearn.worlds import BasicWorld +from pyrobolearn.robots import KukaIIWA + + +# import PyKDL +try: + import PyKDL as kdl +except ImportError as e: + raise ImportError(repr(e) + '\nTry to install `PyKDL`: ' + 'sudo apt-get install ros--python-orocos-kdl' + 'or install it manually from `https://github.com/orocos/orocos_kinematics_dynamics`') + +# import kdl_parser_py +try: + import kdl_parser_py.urdf as KDLParser +except ImportError as e: + raise ImportError(repr(e) + '\nTry to install `kdl_parser_py`: ' + 'sudo apt-get install ros--kdl-parser-py') + +# import track_ik_python +try: + from trac_ik_python.trac_ik import IK as TracIK +except ImportError as e: + raise ImportError(repr(e) + '\nTry to install `trac_ik_python`: ' + 'sudo apt-get install ros--trac-ik-python') + +# import rbdl +try: + import rbdl +except ImportError as e: + raise ImportError(repr(e) + '\nTry to install `rbdl` manually from `https://bitbucket.org/rbdl/rbdl`') + + +# TO BE SET BY THE USER +# select IK solver, by setting the flag: +# 0 = pybullet + calculate_inverse_kinematics() +# 1 = pybullet + damped-least-squares IK using Jacobian (provided by pybullet) +# 2 = PyKDL +# 3 = trac_ik +# 4 = rbdl + damped-least-squares IK using Jacobian (provided by rbdl) +solver_flag = 1 # 1 and 4 gives pretty good results + + +# Create simulator +sim = Bullet() + +# create world +world = BasicWorld(sim) + +# create robot +robot = KukaIIWA(sim) + +# define useful variables for IK +dt = 1./240 +link_id = robot.get_end_effector_ids(end_effector=0) +joint_ids = robot.joints # actuated joint +base_name = robot.base_name +end_effector_name = robot.get_link_names(link_id) +urdf = os.path.dirname(os.path.abspath(__file__)) + '/../../../pyrobolearn/robots/urdfs/kuka/kuka_iiwa/iiwa14.urdf' +damping = 0.01 # for damped-least-squares IK +wrt_link_id = -1 # robot.get_link_ids('iiwa_link_1') +chain_name = robot.get_link_names(joint_ids) + +# desired position +xd = np.array([0.5, 0., 0.5]) +world.load_visual_sphere(xd, radius=0.05, color=(1, 0, 0, 0.5)) + +# joint_ids = joint_ids[2:] + +# print information about the robot +print("") +print("Robot: {}".format(robot)) +print("Number of DoFs: {}".format(robot.num_dofs)) +print("Joint ids: {}".format(robot.joints)) +print("Q Indices: {}".format(robot.get_q_indices())) +print("Actuated joint ids: {}".format(robot.joints)) +print("Link names: {}".format(robot.get_link_names(robot.joints))) +print("End-effector names: {}".format(robot.get_link_names(robot.get_end_effector_ids()))) +print("Floating base? {}".format(robot.has_floating_base())) +print("Total mass = {} kg".format(robot.mass)) +print("") +print("Base name for IK: {}".format(base_name)) +print("Link name for IK: {}".format(end_effector_name)) +print("Chain: {}".format(chain_name)) +print("") + + +robot.change_transparency() +robot.draw_link_frames([-1, 0]) +robot.draw_bounding_boxes(joint_ids[0]) +# robot.draw_link_coms([-1,0]) + +qIdx = robot.get_q_indices(joint_ids) + +print(qIdx) +print(joint_ids) + + +##################### +# IK using pybullet # +##################### + +# OPTION 1: using `calculate_inverse_kinematics`### +if solver_flag == 0: + for _ in count(): + # # get current position in the task/operational space + # x = robot.get_link_positions(link_id, wrt_link_id) + x = robot.get_link_world_positions(link_id) + # print("(xd - x) = {}".format(xd - x)) + + # perform full IK + q = robot.calculate_inverse_kinematics(link_id, position=xd) + + # set the joint positions + robot.set_joint_positions(q[qIdx], joint_ids) + + # step in simulation + world.step(sleep_dt=dt) + +# OPTION 2: using Jacobian and manual damped-least-squares IK ### +elif solver_flag == 1: + kp = 50 # 5 if velocity control, 50 if position control + kd = 0 # 2*np.sqrt(kp) + + for _ in count(): + # get current position in the task/operational space + # x = robot.get_link_positions(link_id, wrt_link_id) + # dx = robot.get_link_linear_velocities(link_id, wrt_link_id) + x = robot.get_link_world_positions(link_id) + dx = robot.get_link_world_linear_velocities(link_id) + print("(xd - x) = {}".format(xd - x)) + + # Get joint configuration + q = robot.get_joint_positions() + + # Get linear jacobian + if robot.has_floating_base(): + J = robot.get_linear_jacobian(link_id, q=q)[:, qIdx + 6] + else: + J = robot.get_linear_jacobian(link_id, q=q)[:, qIdx] + + # Pseudo-inverse + # Jp = robot.get_pinv_jacobian(J) + # Jp = J.T.dot(np.linalg.inv(J.dot(J.T) + damping*np.identity(3))) # this also works + Jp = robot.get_damped_least_squares_inverse(J, damping) + + # evaluate damped-least-squares IK + dq = Jp.dot(kp * (xd - x) - kd * dx) + + # set joint velocities + # robot.set_joint_velocities(dq) + + # set joint positions + q = q[qIdx] + dq * dt + robot.set_joint_positions(q, joint_idss=joint_ids) + + # step in simulation + world.step(sleep_dt=dt) + + +################## +# IK using PyKDL # +################## +elif solver_flag == 2: + print("Using PyKDL:") + model = KDLParser.treeFromFile(urdf) + if model[0]: + model = model[1] + else: + raise ValueError("Error during the parsing") + + # define the kinematic chain + chain = model.getChain(base_name, end_effector_name) + print("Number of joints in the chain: {}".format(chain.getNrOfJoints())) + + # define the FK solver + FK = kdl.ChainFkSolverPos_recursive(chain) + + # define the IK Solver + # IKV = kdl.ChainIkSolverVel_pinv(chain) + # IK = kdl.ChainIkSolverPos_NR(chain, FK, IKV) + IK = kdl.ChainIkSolverPos_LMA(chain) # ,_maxiter=ik_max_iter, _eps_joints=ik_tol) + + # desired final cartesian position + Fd = kdl.Frame(kdl.Vector(xd[0], xd[1], xd[2])) + + for _ in count(): + # get current position in the task/operational space + # x = robot.get_link_positions(link_id, wrt_link_id) + x = robot.get_link_world_positions(link_id) + print("(xd - x) = {}".format(xd - x)) + + # buffer to put the solution + q_solved = kdl.JntArray(chain.getNrOfJoints()) + + # initial joint positions + q = robot.get_joint_positions(joint_ids) + q_init = kdl.JntArray(chain.getNrOfJoints()) + for i, j in enumerate(q): + q_init[i] = j + + # Solve IK + IK.CartToJnt(q_init, Fd, q_solved) + q_solved = np.array([q_solved[i] for i in range(q_solved.rows())]) + + # set joint positions + robot.set_joint_positions(q_solved.tolist(), joint_ids) + + # step in simulation + world.step(sleep_dt=dt) + + +##################### +# IK using track_ik # +##################### +elif solver_flag == 3: + # Documentation: https://bitbucket.org/traclabs/trac_ik/src/master/trac_ik_python/ + # read urdf + urdf_string = open(urdf, 'r').read() + + # create IK solver + ik_solver = TracIK(base_link=base_name, tip_link=end_effector_name, urdf_string=urdf_string, solve_type='Distance') + + # define upper and lower limits (optional) + # lb, ub = -np.ones(6)*100, np.ones(6)*100 + # ik_solver.set_joint_limits(lb, ub) + + for _ in count(): + # get current position in the task/operational space + # x = robot.get_link_positions(link_id, wrt_link_id) + x = robot.get_link_world_positions(link_id) + print("(xd - x) = {}".format(xd - x)) + + # get current joint configuration and orientation (the orientation has to be specified when using trac_ik) + q = robot.get_joint_positions(joint_ids) + quat = robot.get_link_world_orientations(link_id) + + # get solution + q = ik_solver.get_ik(q, x=xd[0], y=xd[1], z=xd[2], rx=quat.x, ry=quat.y, rz=quat.z, rw=quat.w) + + # set joint positions + if q is not None: + q = np.array(q) + robot.set_joint_positions(q, joint_ids) + else: + print('got None') + + # step in the simulation + world.step(sleep_dt=dt) + + +###################################################### +# IK using RBDL and own damped-least-squares inverse # +###################################################### +elif solver_flag == 4: + # load model using rbdl + model = rbdl.loadModel(urdf, verbose=False, floating_base=False) + rbdl_link_id = model.GetBodyId('iiwa_link_7') # end_effector_name) + rbdl_id = [model.GetBodyId(name) - 1 for name in chain_name] + print("RBDL Link ID: {}".format(rbdl_id)) + print("RBDL Q size: {}".format(model.q_size)) + print("RBDL number of DoFs: {}".format(model.dof_count)) + + J = np.zeros((3, model.dof_count)) + + def position_pd(x, xd, v, vd=np.zeros(3), ad=np.zeros(3), kp=100, kd=None): + # if damping is not specified, make it critically damped + if kd is None: + kd = 2.0 * np.sqrt(kp) + + # return PD error + return kp * (xd - x) + kd * (vd - v) + ad + + def damped_least_squares_ik(q, x, xd, v, damping, dt, kp=1, kd=None): + err = position_pd(x, xd, v, kp=kp, kd=kd) + body_point = np.zeros(3) + rbdl.CalcPointJacobian(model, q, rbdl_link_id, body_point, J, update_kinematics=True) + J_dagger = J.T.dot(np.linalg.inv(J.dot(J.T) + damping*np.identity(3))) + dq = J_dagger.dot(err) + q = q + dq * dt + return q + + for _ in count(): + # get current position in the task/operational space + # x = robot.get_link_positions(link_id, wrt_link_id) + x = robot.get_link_world_positions(link_id) + dx = robot.get_link_world_linear_velocities(link_id) + print("(xd - x) = {}".format(xd - x)) + + # get joint configuration + q = robot.get_joint_positions() + + # get solution by performing damped-least-squares IK + q = damped_least_squares_ik(q, x, xd, dx, damping=0., dt=dt, kp=50, kd=0) + + # set the joint positions + robot.set_joint_positions(q[rbdl_id], joint_ids) + + # step in simulation + world.step(sleep_dt=dt) diff --git a/examples/kinematics/inverse/moving_sphere.py b/examples/kinematics/inverse/moving_sphere.py new file mode 100644 index 0000000..9fa12d9 --- /dev/null +++ b/examples/kinematics/inverse/moving_sphere.py @@ -0,0 +1,75 @@ +#!/usr/bin/env python +"""Inverse kinematics with the Kuka robot where the goal is to follow a moving sphere. +""" + +import numpy as np +from itertools import count + +from pyrobolearn.simulators import Bullet +from pyrobolearn.worlds import BasicWorld +from pyrobolearn.robots import KukaIIWA, Body + + +# Create simulator +sim = Bullet() + +# create world +world = BasicWorld(sim) + +# create robot +robot = KukaIIWA(sim) +robot.print_info() + +# define useful variables for IK +dt = 1./240 +link_id = robot.get_end_effector_ids(end_effector=0) +joint_ids = robot.joints # actuated joint +damping = 0.01 # for damped-least-squares IK +wrt_link_id = -1 # robot.get_link_ids('iiwa_link_1') +qIdx = robot.get_q_indices(joint_ids) + +# define gains +kp = 50 # 5 if velocity control, 50 if position control +kd = 0 # 2*np.sqrt(kp) + +# create sphere to follow +sphere = world.load_visual_sphere(position=np.array([0.5, 0., 1.]), radius=0.05, color=(1, 0, 0, 0.5)) +sphere = Body(sim, body_id=sphere) + +# set initial joint positions (based on the position of the sphere at [0.5, 0, 1]) +robot.reset_joint_states(q=[8.84305270e-05, 7.11378917e-02, -1.68059886e-04, -9.71690439e-01, 1.68308810e-05, + 3.71467111e-01, 5.62890805e-05]) + +# define amplitude and angular velocity when moving the sphere +w = 0.01 +r = 0.2 + +for t in count(): + # move sphere + sphere.position = np.array([0.5, r * np.cos(w*t + np.pi/2), (1.-r) + r * np.sin(w*t + np.pi/2)]) + + # get current end-effector position and velocity in the task/operational space + x = robot.get_link_world_positions(link_id) + dx = robot.get_link_world_linear_velocities(link_id) + + # Get joint positions + q = robot.get_joint_positions() + + # Get linear jacobian + if robot.has_floating_base(): + J = robot.get_linear_jacobian(link_id, q=q)[:, qIdx + 6] + else: + J = robot.get_linear_jacobian(link_id, q=q)[:, qIdx] + + # Pseudo-inverse + Jp = robot.get_damped_least_squares_inverse(J, damping) + + # evaluate damped-least-squares IK + dq = Jp.dot(kp * (sphere.position - x) - kd * dx) + + # set joint positions + q = q[qIdx] + dq * dt + robot.set_joint_positions(q, joint_ids=joint_ids) + + # step in simulation + world.step(sleep_dt=dt) diff --git a/pyrobolearn/robots/robot.py b/pyrobolearn/robots/robot.py index 0b96bbe..80ab6c4 100644 --- a/pyrobolearn/robots/robot.py +++ b/pyrobolearn/robots/robot.py @@ -1546,7 +1546,7 @@ class Robot(ControllableBody): # remove parent index from the end-effectors dict if present end_effectors.pop(parent_idx, None) - self.end_effectors = end_effectors.keys() + self.end_effectors = list(end_effectors.keys()) self.end_effector_names = {name: idx for idx, name in end_effectors.items()} def get_end_effector_ids(self, end_effector=None):