ROBOTICS — KINEMATICS, SOFTWARE, AUTONOMY, EMBODIMENT

What we mean by "robot"

A robot is a programmable physical system that senses, plans, and acts. The word was coined by Karel Čapek's brother Josef for the 1920 play R.U.R., from the Czech robota (forced labor). Practical robotics dates from the 1954 patent of the first programmable manipulator by George Devol — the Unimate, deployed at GM in 1961 to handle die-cast parts.

Selected milestones

Forward and inverse kinematics

The Denavit–Hartenberg convention encodes each joint with four parameters (a, α, d, θ) and chains 4×4 transforms.

T_base→tool = A_1 · A_2 · ... · A_n
A_i = Rot_z(θ_i) · Trans_z(d_i) · Trans_x(a_i) · Rot_x(α_i)

Inverse kinematics — solving for joint angles given a desired tool pose — is generically multi-solution and handled numerically (Newton-Raphson, damped least squares) or analytically for solvable manipulators.

The Robot Operating System

ROS (2007, Willow Garage; ROS 2 from 2017) is not an OS but a middleware: a graph of nodes communicating over named topics with publish/subscribe and request/response. It standardized perception, control, and SLAM stacks across labs and industry.

# publish a velocity command (ROS 2, rclpy)
import rclpy
from geometry_msgs.msg import Twist
rclpy.init()
node = rclpy.create_node('drive')
pub  = node.create_publisher(Twist, '/cmd_vel', 10)
msg  = Twist(); msg.linear.x = 0.5; msg.angular.z = 0.2
pub.publish(msg)

Sensors and perception

From A* to MPC

Classical motion planning: A*, Dijkstra, RRT/RRT*, PRM. Trajectory optimization (CHOMP, TrajOpt) treats the path as a continuous variable. Modern model-predictive control (MPC) and differentiable physics simulators have pulled planning toward learned dynamics.

The factory floor

The "big four" industrial robot makers — FANUC, Yaskawa, ABB, KUKA — together control most of the global market. Annual installations crossed 600,000 units in 2024 (IFR). Collaborative robots ("cobots") from Universal Robots (2008) opened lower-payload, fenceless deployment.

Mobile autonomy

The 2005 DARPA Grand Challenge — Stanford's "Stanley" finishing 132 mi of desert in 6h54m — kicked off the modern self-driving stack: HD maps, multi-modal perception, behavior prediction, and safety cases.

Waymo opened robotaxi service in Phoenix in 2018 and reported 250,000+ weekly paid rides across multiple cities by May 2025. Cruise withdrew its San Francisco service in late 2023 after a serious incident.

As of 2026, fully driverless commercial service exists in Phoenix, San Francisco, Los Angeles, Austin, and several Chinese cities (Beijing, Wuhan).

The hard problem

Locomotion looks superhuman; manipulation lags. Real-world objects are partially observable, deformable, and friction-dependent. Recent advances:

• Learning from demonstration — RT-1, RT-2, OpenVLA tie vision-language models to action.
• Diffusion policies (Chi et al., 2023) sample trajectories conditioned on observations.
• Tactile sensing — GelSight, DIGIT, BioTac.
• Sim-to-real with domain randomization (Tobin 2017) and large-scale parallel sim (Isaac Gym, MuJoCo MJX).

The humanoid wave

2022–2026 saw a sudden glut of bipedal humanoids: Tesla Optimus, Figure 01/02, 1X NEO, Apptronik Apollo, Unitree H1, Boston Dynamics' electric Atlas (2024). Drivers: cheap actuators, learned whole-body control, and a labor-shortage thesis in logistics and manufacturing.

Learning + physics

RL in simulation now drives many real-world locomotion controllers (ANYmal, Spot, humanoids). The recipe: massive parallelization in GPU-accelerated simulators, randomize physics, distill to a small policy network, deploy on-robot.

# conceptual
for step in range(10**9):
    obs   = sim.get_obs()
    a     = policy(obs)
    obs2, r = sim.step(a)
    buffer.add(obs, a, r, obs2)
    if step % K == 0: ppo_update(policy, buffer)

Glossary

Recommended viewing

Watch: robotics manipulation research

Open problems

• General-purpose dexterity at human-hand level cost and reliability.
• Robust long-horizon autonomy without expensive teleoperation fallback.
• Safe physical HRI in unstructured human environments.
• Battery energy density limiting humanoid runtime to a few hours.
• A common "ImageNet of manipulation" for learning at scale.