Locomotion

A robot that cannot move through the world has extremely limited utility. Locomotion — the ability to propel oneself through an environment — is what makes a robot a mobile agent rather than a fixed tool. But locomotion is not a single problem: a wheeled robot navigating a flat warehouse floor faces fundamentally different physics than a legged robot traversing rubble, and a drone navigating a building faces different dynamics still. Each locomotion strategy makes different tradeoffs between stability, efficiency, terrain adaptability, and control complexity.

Wheeled Locomotion

Wheeled robots are the dominant form in structured, flat environments — warehouses, factories, hospitals, and roads. Wheels offer high efficiency (rolling friction is much lower than sliding friction), mechanical simplicity, and mature control theory. The most common wheeled configuration for mobile robots is the differential drive: two independently motorized wheels on a common axis, with passive casters for stability. Driving both wheels at the same speed moves straight; driving them at different speeds turns. The radius of curvature R = d * (v_r + v_l) / (2 * (v_r - v_l)), where d is the wheelbase and v_r, v_l are the right and left wheel speeds. This is the same principle a tank uses to steer. Differential drive has a kinematic constraint: it cannot move sideways (it is non-holonomic). To move from one point to another at a different orientation, it must follow a curved path, not translate directly. Holonomic wheeled robots use omnidirectional wheels (mecanum or omniwheels) — wheels with passive rollers at angles that allow lateral motion. Many modern warehouse robots and soccer-playing robots use mecanum wheels for their ability to move in any direction without rotating first. The key control challenge in wheeled locomotion is odometry: estimating position from wheel encoder readings. Wheel slip, encoder quantization, and uneven terrain cause accumulated drift. Wheeled robots that navigate long distances must fuse odometry with other sensors (LIDAR, cameras, GPS) to correct drift — this is the localization problem that connects to the SLAM (Simultaneous Localization and Mapping) techniques discussed in other modules.

Legged locomotion — walking, running, hopping — enables access to terrain where wheels cannot go: stairs, rubble, uneven ground, ladders. Nature's most agile locomotors are all legged: insects, birds, mammals. But legs introduce enormous control complexity that wheels sidestep entirely. The fundamental challenge of legged locomotion is balance. A wheel robot on a flat surface is statically stable — it will not fall even if you turn off the motors. A bipedal (two-legged) robot like a human is statically unstable: a standing human has its center of mass above a small support polygon, and without constant active balance correction, it falls. Stability in legged locomotion is analyzed through the concept of the zero-moment point (ZMP): the point on the ground where the net ground reaction forces produce zero moment. If the ZMP lies within the support polygon (the convex hull of the contact points), the robot is statically stable and will not tip. Classical humanoid robots like Honda's ASIMO were designed to always keep their ZMP inside the support polygon — which forced them to move slowly and avoid configurations where stability would be compromised. Dynamic locomotion, used by Boston Dynamics' Atlas and Spot, abandons static stability. The robot is allowed to be momentarily unstable — like a running human — and the controller continuously recovers balance through fast-reaction stepping and posture adjustment. This allows much faster, more agile locomotion at the cost of much more complex real-time control.

Aerial locomotion — drones and unmanned aerial vehicles (UAVs) — provides access to three-dimensional space inaccessible to ground robots. The dominant platform is the multirotor: a quadrotor (four rotors), hexarotor, or octorotor. Multirotors are mechanically simple, highly maneuverable, and hoverable, but they are energy-intensive (fighting gravity constantly) and fail catastrophically if a motor stops. A quadrotor is controlled by varying the speed (and therefore thrust) of its four rotors. Two pairs rotate clockwise and counterclockwise; the net torques cancel, and the robot does not spin. Increasing all four rotor speeds equally produces upward thrust. Spinning one pair faster than the other produces yaw rotation. Tilting the thrust vector (by spinning some rotors faster than others asymmetrically) produces pitch and roll, which translates to lateral acceleration. The dynamics of a quadrotor are fast (millisecond timescales for attitude stabilization) and require high-frequency control loops — typically 500 Hz to 1 kHz for attitude, with an outer position loop at 50-100 Hz. The attitude stabilization is handled by PID loops on roll, pitch, and yaw — exactly the PID control from Lesson 4, running at very high frequency on an embedded microcontroller. A flight controller chip like the Betaflight or Ardupilot systems implement exactly this architecture.