robotics

name	robotics
description	Robotics design and programming
license	MIT
compatibility	opencode
metadata	{"audience":"engineers, programmers, students","category":"engineering"}

What I do

• Design robot kinematics and dynamics
• Develop motion planning algorithms
• Program robot controllers
• Implement perception and localization
• Create robot simulation environments

When to use me

• When designing robotic systems
• When programming robot movements
• When implementing perception algorithms
• When working with robot kinematics
• When simulating robot behavior

Key Concepts

Forward Kinematics

import numpy as np

class RobotArm:
    def __init__(self, dh_params):
        """DH parameters: [theta, d, a, alpha]"""
        self.dh = dh_params
        self.joints = len(dh_params)
    
    def forward_kinematics(self, joint_angles):
        """Calculate end-effector pose from joint angles"""
        T = np.eye(4)
        
        for i, (theta, d, a, alpha) in enumerate(self.dh):
            # Update theta with joint angle
            theta += joint_angles[i]
            
            # DH transformation matrix
            ct = np.cos(theta)
            st = np.sin(theta)
            ca = np.cos(alpha)
            sa = np.sin(alpha)
            
            T_i = np.array([
                [ct, -st*ca, st*sa, a*ct],
                [st, ct*ca, -ct*sa, a*st],
                [0, sa, ca, d],
                [0, 0, 0, 1]
            ])
            
            T = T @ T_i
        
        return T
    
    def jacobian(self, joint_angles):
        """Compute Jacobian matrix"""
        # Geometric Jacobian method
        pass

Inverse Kinematics

class InverseKinematics:
    @staticmethod
    def analytical_ik_2link(target, L1, L2):
        """2-link planar arm analytical solution"""
        x, y = target
        
        # Cosine rule
        cos_theta2 = (x**2 + y**2 - L1**2 - L2**2) / (2 * L1 * L2)
        cos_theta2 = np.clip(cos_theta2, -1, 1)
        
        theta2 = np.arccos(cos_theta2)
        theta1 = np.arctan2(y, x) - np.arctan2(
            L2 * np.sin(theta2), 
            L1 + L2 * np.cos(theta2)
        )
        
        return [theta1, theta2]
    
    @staticmethod
    def numerical_ik(forward_fn, target_pose, initial_joints, max_iter=100):
        """Numerical IK using Jacobian pseudo-inverse"""
        joints = np.array(initial_joints)
        
        for _ in range(max_iter):
            current_pose = forward_fn(joints)
            error = target_pose - current_pose
            
            if np.linalg.norm(error) < 1e-6:
                break
            
            J = self.jacobian(joints)
            delta_joints = J.T @ np.linalg.pinv(J @ J.T + 0.01) @ error
            joints += delta_joints
        
        return joints

Motion Planning

class MotionPlanner:
    @staticmethod
    def rrt(start, goal, obstacles, max_iter=1000):
        """Rapidly-exploring Random Tree"""
        tree = [start]
        
        for _ in range(max_iter):
            # Random sample
            if np.random.rand() < 0.1:
                sample = goal
            else:
                sample = random_configuration()
            
            # Find nearest
            nearest = tree[np.argmin([dist(n, sample) for n in tree])]
            
            # Steer towards sample
            new = steer(nearest, sample)
            
            if not collision(new, obstacles):
                tree.append(new)
                
                if dist(new, goal) < threshold:
                    return reconstruct_path(tree, start, goal)
        
        return None
    
    @staticmethod
    def trajectory_smooth(waypoints, resolution=0.01):
        """Smooth trajectory using splines"""
        from scipy.interpolate import splprep, splev
        
        tck, u = splprep(waypoints, s=0)
        smoothed = splev(np.linspace(0, 1, 100), tck)
        return smoothed

Robot Controllers

# PID joint controller
class JointController:
    def __init__(self, kp, ki, kd):
        self.kp = kp
        self.ki = ki
        self.kd = kd
        self.integral = 0
        self.prev_error = 0
    
    def compute(self, setpoint, measurement, dt):
        error = setpoint - measurement
        self.integral += error * dt
        derivative = (error - self.prev_error) / dt
        
        output = self.kp * error + self.ki * self.integral + self.kd * derivative
        self.prev_error = error
        
        return output

# Impedance control
class ImpedanceController:
    def __init__(self, M, B, K):
        self.M = M  # Mass matrix
        self.B = B  # Damping
        self.K = K  # Stiffness
    
    def compute_force(self, desired_pos, actual_pos, velocity):
        # F = M*acc_d + B*(v_d - v) + K*(x_d - x)
        error = desired_pos - actual_pos
        force = -self.B @ velocity - self.K @ error
         force

Perception

# Object detection basics
class PerceptionSystem:
    def __init__(self):
        self.camera = None
        self.lidar = None
        self.depth_sensor = None
    
    def point_cloud_to_image(self, points, camera_matrix):
        """Project 3D points to 2D image"""
        # Apply camera extrinsics and intrinsics
        pass
    
    def detect_objects(self, point_cloud):
        """Detect objects in point cloud"""
        # Use clustering (DBSCAN, Euclidean)
        # Classify clusters
        pass
    
    def estimate_pose(self, object_points, image_points, camera_matrix):
        """PnP pose estimation"""
        # Perspective-n-Points algorithm
        pass

ROS Basics

# ROS 2 Python node
class ROS2Node:
    def __init__(self, node_name):
        self.node_name = node_name
        self.pubs = {}
        self.subs = {}
    
    def create_publisher(self, topic, msg_type):
        """Create publisher"""
        pass
    
    def create_subscription(self, topic, msg_type, callback):
        """Create subscriber"""
        pass
    
    def spin(self):
        """Process callbacks"""
        pass

Robot Types

Type	Characteristics	Applications
Articulated	Multiple rotating joints	Manufacturing, welding
SCARA	Horizontal articulated	Pick and place
Delta	Parallel mechanism	High speed assembly
Cartesian	Linear axes	CNC, 3D printing
Mobile	Moving base	Delivery, exploration
Humanoid	Bipedal	Research, assistance