How to Control Robot Arms: Kinematics, Dynamics, and Force Feedback

Step-by-Step Guide

1. 1

   Understand Robot Arm Kinematics

   A robot arm is a chain of links connected by joints. Each joint adds one DOF. A 6-DOF arm can reach any position and orientation. Forward kinematics computes end-effector position from joint angles (matrix multiplication). Inverse kinematics computes joint angles for a target position — harder, may have multiple solutions.

   python Copy

   # Forward kinematics using DH parameters
   import numpy as np
   
   def dh_transform(theta, d, a, alpha):
       return np.array([
           [np.cos(theta), -np.sin(theta)*np.cos(alpha), np.sin(theta)*np.sin(alpha), a*np.cos(theta)],
           [np.sin(theta), np.cos(theta)*np.cos(alpha), -np.cos(theta)*np.sin(alpha), a*np.sin(theta)],
           [0, np.sin(alpha), np.cos(alpha), d], [0, 0, 0, 1]])
   
   def fk_2dof(theta1, theta2, l1, l2):
       T1 = dh_transform(theta1, 0, l1, 0)
       T2 = dh_transform(theta2, 0, l2, 0)
       return (T1 @ T2)[:2, 3]

2. 2

   Master DH Parameters

   DH parameters describe robot arm geometry: theta (joint angle), d (link offset), a (link length), alpha (link twist). Assign frames to each link following DH conventions, then build the transformation chain.

   💡

   Tip: Use modified DH parameters (Craig convention) — more intuitive and widely used in modern robotics textbooks.
3. 3

   Solve Inverse Kinematics

   IK finds joint angles for a target. Analytical solutions exist for simple arms (2-DOF planar) and 6-DOF arms with spherical wrists. For general cases, use numerical methods: Jacobian pseudo-inverse, CCD, or TRAC-IK. MoveIt2 provides production-ready IK.

   python Copy

   # Analytical IK for 2-DOF planar arm
   import numpy as np
   def ik_2dof(x, y, l1, l2):
       c2 = (x**2 + y**2 - l1**2 - l2**2) / (2*l1*l2)
       if abs(c2) > 1: raise ValueError("Out of reach")
       t2 = np.arccos(c2)
       t1 = np.arctan2(y, x) - np.arctan2(l2*np.sin(t2), l1+l2*np.cos(t2))
       return t1, t2

4. 4

   Understand the Jacobian

   The Jacobian J maps joint velocities to end-effector velocities: ẋ = J·θ̇. Used for velocity control, force transformation (τ = Jᵀ·F), and singularity detection (det(J)=0). Singularities occur when the arm loses a DOF.

   ⚠️

   Warning: Near singularities, small Cartesian velocities require huge joint velocities. Use damped least-squares (DLS) inverse for numerical stability.
5. 5

   Implement PID Position Control

   PID control drives each joint motor to track a desired position. P reduces rise time, I eliminates steady-state error, D reduces overshoot. For robot arms, cascaded PID (position → velocity → torque) provides better performance.

   python Copy

   class PID:
       def __init__(self, kp, ki, kd):
           self.kp, self.ki, self.kd = kp, ki, kd
           self.integral = 0
           self.prev_error = 0
       def update(self, setpoint, measurement, dt):
           error = setpoint - measurement
           self.integral += error * dt
           deriv = (error - self.prev_error) / dt
           self.prev_error = error
           return self.kp*error + self.ki*self.integral + self.kd*deriv

6. 6

   Generate and Track Trajectories

   Trajectory generation creates smooth motion between waypoints: polynomial interpolation (quintic for smooth velocity/acceleration), trapezoidal velocity profiles, B-splines. Use computed torque control or PID feedback for tracking. MoveIt2 handles trajectory generation and collision checking.

   💡

   Tip: Use quintic polynomial interpolation — continuous position, velocity, and acceleration, minimizing jerk and reducing joint wear.
7. 7

   Implement Force/Torque Control

   Position control cannot handle contact tasks (assembly, polishing). Force control regulates contact force. Hybrid force/position control: force in constrained directions, position in free directions. Impedance control: arm behaves like a spring-damper. Force/torque sensors (ATI, OnRobot) measure contact forces.

   

8. 8

   Use MoveIt2 for Motion Planning

   MoveIt2 is the standard ROS2 motion planning framework: IK solvers, OMPL planning, FCL collision checking, trajectory execution, RViz2 visualization. Configure with your URDF, then use the MoveGroup action interface.

   python Copy

   # MoveIt2 Python interface
   import rclpy
   from moveit.planning import MoveItPy
   rclpy.init()
   moveit = MoveItPy(node_name="moveit_py")
   arm = moveit.get_planning_component("arm")
   arm.set_pose_target([0.3, 0.2, 0.5, 0.0, 0.0, 0.0])
   plan = arm.plan()
   if plan.planning_result.success:
       arm.execute(plan.trajectory)

9. 9

   Implement Compliant Control

   Compliant control makes arms safe for human interaction. Admittance control: measure force, compute position offset, command to position controller. Impedance control: regulate force-motion relationship. Variable stiffness: adjust compliance by task phase. Essential for cobots.

   ⚠️

   Warning: Industrial robots with high stiffness and no force sensing are dangerous to humans. Cobots (UR, Franka, KUKA iiwa) use torque sensors and compliant control for safe collaboration.
10. 10

    Calibrate and Identify Dynamics

    Dynamic model: τ = M(q)·q̈ + C(q,q̇)·q̇ + G(q) + F. M=inertia, C=Coriolis, G=gravity, F=friction. Accurate dynamics enable computed torque control and force estimation. Identify parameters via least-squares from trajectory data.

    text Copy

    Robot Arm Dynamics:
    τ = M(q)·q̈ + C(q,q̇)·q̇ + G(q) + F(q̇)
    M: inertia matrix, C: Coriolis, G: gravity, F: friction
    Computed Torque: τ = M(q)·(q̈_d + Kp·e + Kd·ė) + C·q̇ + G

11. 11

    Integrate Grasping

    Gripper types: parallel jaw (reliable), vacuum (fast, flat objects), soft (adaptive, fragile). Grasp planning: antipodal grasping, Dex-Net database, GraspNet deep learning. Pipeline: approach, grasp, lift, transport, place.

    

12. 12

    Deploy to a Real Robot

    Simulation to real requires: accurate URDF, calibrated kinematics, tuned PID gains, safety limits. Use ros2_control for hardware abstraction. Start with 10% speed and increase gradually.

    ⚠️

    Warning: Never deploy without testing in simulation first (Gazebo, Isaac Sim). Verify joint limits, collision avoidance, and e-stop. A controller bug can cause violent motion.