std.robotics — Kinematics & Autonomous Motion Control

Enterprise robotics engineering: Denavit-Hartenberg (DH) parameter forward kinematics, minimum-jerk quintic trajectory splines, and anti-windup PID joint controllers.

1. 6-DOF Robot Arm Forward Kinematics

Model serial manipulators and compute end-effector Cartesian poses $(X, Y, Z)$ using standard DH parameters:

import std.robotics.kinematics
import std.io

pub fn main() {
    let mut arm = kinematics.create_robot_arm("UR10e-Enterprise")
    
    // Add 6 standard rotational joints (theta, d, a, alpha)
    kinematics.add_joint(&mut arm, 0.1625, 0.0, 1.5708, 0.0)
    kinematics.add_joint(&mut arm, 0.0, -0.425, 0.0, -1.5708)
    kinematics.add_joint(&mut arm, 0.0, -0.3922, 0.0, 0.0)
    kinematics.add_joint(&mut arm, 0.1333, 0.0, 1.5708, 0.0)
    kinematics.add_joint(&mut arm, 0.0997, 0.0, -1.5708, 0.0)
    kinematics.add_joint(&mut arm, 0.0996, 0.0, 0.0, 0.0)

    let pose = kinematics.compute_forward_kinematics(&arm)
    std.io.println("End-Effector Pose: X=" + pose.x.to_string() + 
                   " Y=" + pose.y.to_string() + 
                   " Z=" + pose.z.to_string())
}

2. Minimum-Jerk Quintic Trajectory Planning

Generate smooth $C^2$-continuous trajectory splines with zero starting and ending jerk:

import std.robotics.kinematics
import std.io

pub fn main() {
    let start_pos = 0.0
    let target_pos = 1.5707963 // 90 degrees
    let duration = 5.0 // seconds

    // Evaluate waypoint at t = 2.5s (midpoint)
    let pos_mid = kinematics.evaluate_quintic_trajectory(start_pos, target_pos, duration, 2.5)
    std.io.println("Midpoint Joint Angle: " + pos_mid.to_string() + " rad") // 0.785398 rad
}

3. Cascaded PID Controller with Anti-Windup

import std.robotics.kinematics
import std.io

pub fn main() {
    let mut pid = kinematics.create_pid(45.0, 0.5, 2.1, 100.0)
    let target_pos = 1.5708
    let current_pos = 0.0
    let dt = 0.01

    let torque = kinematics.compute_pid_torque(&mut pid, target_pos, current_pos, dt)
    std.io.println("Calculated Motor Torque: " + torque.to_string() + " Nm")
}