Modified version of the KUKA LWR4 (7 DOF) with an added prismatic joint between the last revolute joint and the end-effector, giving it 8 degrees of freedom. The prismatic joint has a range of 0 to 0.08 m.
Everything runs on ROS Noetic with visualization in RViz. The robot model is defined via URDF/Xacro.
- URDF/Xacro description of the modified robot (8 DOF)
- Forward kinematics (DH parameters)
- Inverse kinematics (Newton-Raphson, numerical)
- Kinematic control (Jacobian-based, position control)
- Dynamics (inertia matrix, Coriolis, gravity via RBDL)
- Two dynamic controllers:
- Inverse dynamics (feedback linearization) — settles in ~37s
- PD + gravity compensation — settles in ~170s
| Joint | d (m) | θ (rad) | a (m) | α (rad) |
|---|---|---|---|---|
| 1 | 0.36 | q₁ + π | 0 | π/2 |
| 2 | 0 | q₂ + π | 0 | π/2 |
| 3 | 0.42 | q₃ | 0 | π/2 |
| 4 | 0 | q₄ + π | 0 | π/2 |
| 5 | 0.40 | q₅ | 0 | π/2 |
| 6 | 0 | q₆ + π | 0 | π/2 |
| 7 (prismatic) | q₇ | 0 | 0 | 0 |
| 8 | 0.10 | q₈ | 0 | π/2 |
Computed from the DH table above. Reference frames verified in RViz:
Example — q = [0, 0, 0, 0, 0, 0, 0, 0]:
Position: [0, 0, 1.38] — the robot is fully extended upward, which matches the sum of link lengths.
Numerical solution using Newton-Raphson. The method iterates until the FK output matches the desired position within a tolerance.
For x_d = [0.5, 0.5, 0.5] it converges in 42 iterations:
Position control using the analytical Jacobian (3×8) and its pseudo-inverse. The prismatic joint (q₇) is clamped in the code since RViz doesn't enforce URDF limits during control.
The controller uses ė* = -k·e with k = 1, integrated via Euler method.
Target: x_d = [0.5, 0.5, 0.5] m
End-effector reaching the target (green marker)
Joint trajectories:
End-effector convergence in X, Y, Z:
X and Z converge well. Y has a small steady-state offset — could be improved with higher gain or a different control strategy.
Robot dynamics computed with RBDL from the URDF: inertia matrix M(q), Coriolis C(q,q̇)q̇, and gravity g(q).
Full model compensation:
u = M(q)(q̈_d + Kd(q̇_d − q̇) + Kp(q_d − q)) + C(q,q̇)q̇ + g(q)
Settles in about 37 seconds:
Simpler controller — only compensates gravity:
u = g(q) + Kp(q_d − q) − Kd·q̇
Settles in about 170 seconds (much slower, but simpler to implement):
The inverse dynamics controller is roughly 4.5x faster since it compensates the full nonlinear dynamics, not just gravity.
Requirements: ROS Noetic, Python 3, RBDL, NumPy
# Clone
git clone https://github.com/josue99999/CONTROL-LWR-4-ROS-NOETIC.git
# Build
cd ~/catkin_ws && catkin_make
# Launch robot in RViz
roslaunch kuka_lbr_iiwa_support display.launch
# Forward kinematics test
rosrun kuka_lbr_iiwa_support test_fkine
# Inverse kinematics
rosrun kuka_lbr_iiwa_support test_ikine_PROYECTO
# Kinematic control
rosrun kuka_lbr_iiwa_support control_cinematico
# Dynamic control — inverse dynamics
rosrun kuka_lbr_iiwa_support control_dinamico_inverso
# Dynamic control — PD + gravity
rosrun kuka_lbr_iiwa_support control_pd_gravedad- The prismatic joint (q₇) starts at its max distance (0.08 m). In dynamic control, if the desired position exceeds this limit, q₇ stays at its physical boundary — this is expected behavior, not a bug.
- Kinematic control only handles position (not orientation) to keep things simpler.
- The Jacobian uses Moore-Penrose pseudo-inverse with a damping factor (λ = 0.01) near singularities.
- Zaplana, I. (2017). Análisis Cinemático de Robots Manipuladores Redundantes
- Corrales, J. (2016). Manipulation and path planning for KUKA (LWR/LBR 4+) robot
- KUKA Robotics — LBR iiwa