NeuralBlitz Robotics
What I Do
I provide comprehensive robotics tools including forward and inverse kinematics, dynamics, motion planning, perception algorithms, control systems, and human-robot interaction for robotics applications.
When to Use Me
- Robot manipulator design
- Mobile robot navigation
- Sensor integration
- Motion planning algorithms
- Robot control systems
- Autonomous systems
Core Concepts
- Kinematics: Forward and inverse kinematics
- Dynamics: Newton-Euler, Lagrangian
- Motion Planning: Path planning, trajectory generation
- Perception: Computer vision, sensor fusion
- Control: PID, adaptive, robust control
- Localization: SLAM, Kalman filtering
- Dynamics: Joint dynamics, workspace analysis
- Human-Robot Interaction: Safety, collaboration
Code Examples
Forward Kinematics
import numpy as np
def dh_transform(theta, d, a, alpha):
ct = np.cos(theta)
st = np.sin(theta)
ca = np.cos(alpha)
sa = np.sin(alpha)
return np.array([
[ct, -st*ca, st*sa, a*ct],
[st, ct*ca, -ct*sa, a*st],
[0, sa, ca, d],
[0, 0, 0, 1]
])
def forward_kinematics(dh_params, joint_angles):
T = np.eye(4)
for i, (theta, d, a, alpha) in enumerate(dh_params):
T = T @ dh_transform(joint_angles[i], d, a, alpha)
return T
dh_params = [
(0, 0.089, 0, np.pi/2),
(0, 0, -0.425, 0),
(0, 0, -0.392, 0)
]
joints = [0, 0, 0]
T = forward_kinematics(dh_params, joints)
print(f"End effector position: {T[:3, 3]}")
Inverse Kinematics
def analytical_ik_2r(link1, link2, target):
x, y = target
D = (x**2 + y**2 - link1**2 - link2**2) / (2 * link1 * link2)
if abs(D) > 1:
return None
theta2 = np.arctan2(np.sqrt(1 - D**2), D)
theta1 = np.arctan2(y, x) - np.arctan2(link2 * np.sin(theta2), link1 + link2 * np.cos(theta2))
return [theta1, theta2]
def numerical_ik(fk_func, target, initial_joints, max_iter=100, tol=1e-4):
joints = np.array(initial_joints)
for _ in range(max_iter):
T = fk_func(joints)
error = target - T[:3, 3]
if np.linalg.norm(error) < tol:
break
J = numerical_jacobian(fk_func, joints)
joints += np.linalg.pinv(J) @ error
return joints
link1, link2 = 1.0, 0.8
target = (1.2, 0.5)
solution = analytical_ik_2r(link1, link2, target)
print(f"Joint angles: {solution}")
Motion Planning
def rrt_planner(start, goal, obstacles, bounds, step_size=0.1, max_iter=1000):
tree = {tuple(start): None}
for _ in range(max_iter):
if np.random.random() < 0.1:
rand_point = tuple(goal)
else:
rand_point = tuple(np.random.uniform(bounds[0], bounds[1]))
nearest = min(tree.keys(), key=lambda x: np.linalg.norm(np.array(x) - np.array(rand_point)))
direction = np.array(rand_point) - np.array(nearest)
direction = direction / np.linalg.norm(direction) * step_size
new_point = tuple(np.array(nearest) + direction)
if not collision_check(nearest, new_point, obstacles):
tree[new_point] = nearest
if np.linalg.norm(np.array(new_point) - np.array(goal)) < step_size:
return reconstruct_path(tree, start, goal)
return None
def astar(start, goal, grid):
open_set = {start}
came_from = {}
g_score = {start: 0}
f_score = {start: heuristic(start, goal)}
while open_set:
current = min(open_set, key=lambda x: f_score.get(x, float('inf')))
if current == goal:
return reconstruct_path(came_from, current)
open_set.remove(current)
for neighbor in get_neighbors(current, grid):
tentative_g = g_score[current] + 1
if tentative_g < g_score.get(neighbor, float('inf')):
came_from[neighbor] = current
g_score[neighbor] = tentative_g
f_score[neighbor] = g_score[neighbor] + heuristic(neighbor, goal)
if neighbor not in open_set:
open_set.add(neighbor)
return None
Robot Dynamics
def compute_inertia_tensor(m, dims, com):
I = np.zeros((3, 3))
I[0, 0] = m/12 * (dims[1]**2 + dims[2]**2)
I[1, 1] = m/12 * (dims[0]**2 + dims[2]**2)
I[2, 2] = m/12 * (dims[0]**2 + dims[1]**2)
return I
def newton_euler_iteration(i, omega, alpha, a, v, joint_type, params):
if joint_type == 'revolute':
Fi = params['I'] @ alpha + np.cross(omega, params['I'] @ omega)
Ni = params['I'] @ alpha + np.cross(omega, params['I'] @ omega)
else:
Fi = params['m'] * (a + np.cross(alpha, params['r']) +
np.cross(omega, np.cross(omega, params['r'])))
Ni = params['I'] @ alpha + np.cross(omega, params['I'] @ omega)
return Fi, Ni
def gravitational_torque(g, M, J):
return -J.T @ M @ g
def compute_dynamic_model(M, C, G, q, dq):
Mq = M(q) @ ddot_q + C(q, dq) + G(q)
return Mq
Kalman Filter for Localization
def kalman_filter(x, P, z, H, R, F, Q):
x_pred = F @ x
P_pred = F @ P @ F.T + Q
K = P_pred @ H.T @ np.linalg.inv(H @ P_pred @ H.T + R)
x_update = x_pred + K @ (z - H @ x_pred)
P_update = (np.eye(len(x)) - K @ H) @ P_pred
return x_update, P_update
def extended_kalman_filter(x, P, z, h, H_func, F_func, Q, R):
x_pred = F_func(x)
P_pred = F_func(x) @ P @ F_func(x).T + Q
H = H_func(x_pred)
K = P_pred @ H.T @ np.linalg.inv(H @ P_pred @ H.T + R)
z_pred = h(x_pred)
x_update = x_pred + K @ (z - z_pred)
P_update = (np.eye(len(x)) - K @ H) @ P_pred
return x_update, P_update
def particle_filter(particles, weights, z, motion_model, measurement_model):
particles = [motion_model(p) for p in particles]
weights = [w * measurement_model(z, p) for w, p in zip(weights, particles)]
weights /= sum(weights)
indices = np.random.choice(len(particles), len(particles), p=weights)
particles = [particles[i] for i in indices]
return particles, weights
Best Practices
- Coordinate Frames: Define and track all frames consistently
- Singularities: Handle kinematic singularities carefully
- Numerical Stability: Use stable algorithms for inverse kinematics
- Safety: Implement safety checks for all motions
- Calibration: Account for calibration errors
Common Patterns
# PID controller
class PIDController:
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, error, dt):
self.integral += error * dt
derivative = (error - self.prev_error) / dt if dt > 0 else 0
self.prev_error = error
return self.kp * error + self.ki * self.integral + self.kd * derivative
Core Competencies
- Kinematics (forward/inverse)
- Motion planning algorithms
- Robot dynamics and control
- Localization and SLAM
- Sensor integration