11.13. Dynamics in Legged and Wheeled Robots

Legged robots (e.g., bipeds, quadrupeds) require complex modeling of: • Multi-body limb systems • Ground reaction forces • ZMP (Zero Moment Point) stability Walking Dynamics are phase-based: stance and swing phases with discontinuities at foot impacts. Control requires: • Whole-body inverse dynamics • Trajectory optimization • Nonlinear predictive control

Legged robots, like those resembling humans or animals, have limbs that move in coordinated ways. To model their movement accurately, engineers consider several factors. These include 'multi-body limb systems,' which represent how each limb interacts with others, and 'ground reaction forces,' the forces exerted by the ground on the robot's feet when walking. Additionally, 'ZMP stability' refers to a specific point where the robot must remain balanced. When a legged robot moves, it goes through two main phases: 'stance' (when the foot is on the ground) and 'swing' (when the foot is in the air). Understanding these phases is crucial because there are sudden changes (discontinuities) when the foot lands or lifts off. To manage all this movement smoothly, control strategies involve whole-body inverse dynamics to calculate the forces needed at each joint, trajectory optimization to plan the robot's path efficiently, and nonlinear predictive control to adjust movements based on predictions of future states.

Think of a person walking up a staircase. As they stand on one leg (the stance phase), that foot pushes against the steps. When they lift the other foot (the swing phase), they have to maintain their balance or risk falling. Like the person, legged robots need to manage their balance and movement carefully, ensuring they land on their feet without tipping over.

Wheeled mobile robots must satisfy non-holonomic constraints (no side slip for standard wheels): Dynamic equations include: • Rolling constraints • Mass and inertia distribution • Terrain interaction models (e.g., rough ground, slopes) Control often uses: • Lyapunov-based methods • Differential drive or Ackermann steering kinematics + dynamics

Wheeled robots, such as cars and robotic delivery devices, have unique dynamics because they are bound by 'non-holonomic constraints.' This means they can only move forward or backward and cannot slide sideways like they might on ice. To accurately represent their motion, engineers create dynamic equations that consider several key aspects: 'rolling constraints' relate to how wheels can roll without slipping, while 'mass and inertia distribution' helps understand how weight affects movement. Additionally, 'terrain interaction models' account for how the robot behaves on different surfaces, like rough roads or slopes. For controlling these robots, methods leveraging Lyapunov's stability theory ensure safe and efficient movement, while techniques like differential drive allow for precise steering and turning.

Imagine riding a bicycle. You can't easily slide sideways; you must balance and steer. Just like a cyclist must lean into turns and pedal up hills, wheeled robots have to adapt their movements to the surface they're on. They rely on carefully crafted controls to ensure they move smoothly and stay on track without slipping.

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