Notes in Week 5- Legged and Wheeled Robots

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Published	11/26/2024	In humanoid robots, {{c1::1-DOF rotational joints}} are typically used for each joint in basic models.
Published	11/26/2024	The base of a humanoid robot, also called the {{c1::pelvis link}}, serves as the global root link in the kinematic chain.
Published	11/26/2024	The term {{c1::floating base}} in robotics refers to a base link that can move freely in 3D space.
Published	11/26/2024	Each robot link’s position and orientation are represented through an attached {{c1::coordinate frame}}.
Published	11/26/2024	For a humanoid robot, the {{c1::3R joint assemblies}} at hips, shoulders, and wrists are modeled as spherical joints (3-DOF).
Published	11/26/2024	The usual structural setup for humanoid robots forms a {{c1::kinematic chain}} where links connect sequentially from the base.
Published	11/26/2024	Humanoid robots often have temporary {{c1::contact joints}} between feet and ground, forming closed loops in the chain.
Published	11/26/2024	The {{c1::inertial frame}} {W} is fixed to the ground in robotic frames, while {B} is fixed to the base of the robot.
Published	11/26/2024	Frames at the terminal links of a robot, such as feet or hands, are critical for {{c1::interaction with the environment}}.
Published	11/26/2024	The four phases in a walking gait cycle include {{c1::double support}}, {{c2::toe-off}}, {{c3::single support}}, and {{c4::heel strike}}.
Published	11/26/2024	A {{c1::support polygon}} defines the horizontal region over which the robot’s center of mass (CoM) must lie to maintain stability.
Published	11/26/2024	A walking robot is in static equilibrium if the projection of its CoM remains within the {{c1::support polygon}}.
Published	11/26/2024	A {{c1::static walk}} keeps the CoM inside the support polygon, while {{c2::dynamic walking}} relies on motion to maintain stability.
Published	11/26/2024	In stable gaits, the CoM projects to the ground within the polygon, maintaining a balance with the {{c1::gravity vector}}.
Published	11/26/2024	Dynamic walking includes periods where the CoM is outside the support polygon, unlike {{c1::statically stable gaits}}.
Published	11/26/2024	The ZMP, or {{c1::Zero Moment Point}}, is the point on the ground where the sum of horizontal forces is zero.
Published	11/26/2024	A support polygon in humanoid walking is defined as the {{c1::convex hull of contact points}} between robot and ground.
Published	11/26/2024	To maintain postural stability, the ZMP-based gait algorithm keeps the {{c1::ZMP inside the support polygon}}.
Published	11/26/2024	For a humanoid robot to remain balanced, the {{c1::Center of Pressure (CoP)}} should lie within the support polygon.
Published	11/26/2024	The {{c1::special Euclidean group SE(3)}} defines the position and orientation of a robot in 3D space.
Published	11/26/2024	For kinematic analysis, the Denavit-Hartenberg notation is often used with {{c1::single-DOF models}}.
Published	11/26/2024	The forward kinematics function describes the end-effector position in terms of the robot’s {{c1::joint angles}}.
Published	11/26/2024	The transformation matrix \( X_T^B \) in forward kinematics describes the position of frame {T} relative to the {{c1::base frame}} {B}.
Published	11/26/2024	Inverse kinematics solves for {{c1::joint angles}} given the end-effector position in the inertial frame.
Published	11/26/2024	A {{c1::closed-form solution}} to the inverse kinematics problem provides exact values for joint variables.
Published	11/26/2024	If no closed-form solution exists, inverse kinematics may use {{c1::numerical methods}} based on differential relationships.
Published	11/26/2024	Humanoid robots use the forward kinematic function to calculate the CoM in terms of the robot's {{c1::joint configuration}}.
Published	11/26/2024	The inverse kinematics problem is often solved for the end-effector to reach a {{c1::specific target position}}.
Published	11/26/2024	The equations of motion for a manipulator include terms for {{c1::inertia}}, {{c2::Coriolis and centrifugal forces}}, and {{c3::gravity}}.
Published	11/26/2024	The {{c1::generalized forces}} acting on a robot are expressed in the form \( D(q) \ddot{q} + C(q, \dot{q}) \dot{q} + G(q) = f \).
Published	11/26/2024	Contact forces during walking can be broken down into {{c1::normal}} and {{c2::tangential}} components.
Published	11/26/2024	Normal contact forces ensure that the robot does not {{c1::penetrate the ground}}, acting as a non-holonomic constraint.
Published	11/26/2024	Frictional forces at the contact surface prevent sliding and are proportional to the {{c1::normal force}}.
Published	11/26/2024	The {{c1::Coulomb friction model}} describes the tangential force as proportional to the normal force, counteracting motion.
Published	11/26/2024	A robot’s Zero Moment Point, ZMP, lies within the support polygon for the robot to remain {{c1::dynamically balanced}}.
Published	11/26/2024	The ZMP-based gait generation involves steps to plan the {{c1::footsteps}}, {{c2::ZMP trajectory}}, and {{c3::CoM trajectory}}.
Published	11/26/2024	Wheeled mobile robots can be classified into two major categories: {{c1::omnidirectional}} and {{c2::nonholonomic}}.
Published	11/26/2024	A kinematic model in robotics describes how {{c1::wheel speeds}} map to robot velocities.
Published	11/26/2024	In modeling wheeled robots, a configuration \( T_B^W \in SE(2) \) represents the robot’s pose relative to a {{c1::fixed world frame}}.
Published	11/26/2024	The pose of a wheeled robot in 2D space is often defined by coordinates \( q = ({{c1::\theta}}, {{c2::x}}, {{c3::y}}) \).
Published	11/26/2024	In nonholonomic robots, the robot's movement is restricted to a specific path and cannot freely move in {{c1::any direction}}.
Published	11/26/2024	Omnidirectional robots are capable of movement in any direction, as they do not have {{c1::nonholonomic constraints}}.
Published	11/26/2024	Nonholonomic constraints limit a robot’s movement, preventing {{c1::lateral motion}} without complex maneuvers.
Published	11/26/2024	The kinematic model for low-speed behavior of a four-wheeled car-like robot is commonly represented by the {{c1::bicycle model}}.
Published	11/26/2024	The rear wheel in a car-like robot is fixed to the body, while the front wheel rotates to steer, known as the {{c1::Ackermann steering model}}.
Published	11/26/2024	The Instantaneous Center of Rotation (ICR) in car-like robots is where the {{c1::wheel directions intersect}}, representing the vehicle’s turning cent…
Published	11/26/2024	For a car-like robot, the equation for heading rate is \( \dot{\theta} = \frac{v}{L} \tan \psi \), where \( v \) is the vehicle's {{c1::velocity}}.
Published	11/26/2024	The steering angle \( \psi \) of the front wheel in car-like robots dictates the minimum turning radius, limiting {{c1::maneuverability}}.
Published	11/26/2024	The Ackermann steering mechanism in cars ensures that front wheels follow different paths, reducing {{c1::wear and tear}} on tires.
Published	11/26/2024	A unicycle robot has a configuration \( q = (\theta, x, y, \phi) \), where \( \theta \) is the {{c1::heading direction}} and \( \phi \) the rolling an…
Published	11/26/2024	In unicycle models, control inputs include \( u_1 = \dot{\phi} \) for {{c1::driving speed}} and \( u_2 = \dot{\theta} \) for turning.
Published	11/26/2024	Differential steering robots achieve turns by controlling the speed of {{c1::wheels on each side}} independently.
Published	11/26/2024	For differential steering, the vehicle’s turn rate is \( \dot{\theta} = \frac{v_R - v_L}{W} \), where \( W \) is the {{c1::wheel separation}}.
Published	11/26/2024	A differential drive robot’s motion is modeled by \( \dot{x} = v \cos \theta \) and \( \dot{y} = v \sin \theta \), assuming no {{c1::slip}}.
Published	11/26/2024	Differentially steered robots can turn on the spot, a type of steering known as {{c1::skid steering}}.
Published	11/26/2024	In skid steering, the wheels turn at different rates, creating a {{c1::lateral component}} that violates the no-slip constraint.
Published	11/26/2024	For differential steering, the vehicle’s path curves along the Instantaneous Center of Rotation (ICR), where {{c1::lateral velocity}} is zero.
Published	11/26/2024	Differentially steered robots employ a {{c1::kinematic unicycle model}} at low speeds, which simplifies modeling.
Published	11/26/2024	Omnidirectional wheels, like mecanum wheels, allow robots to move in any direction by relaxing the {{c1::nonholonomic constraint}}.
Published	11/26/2024	Mecanum wheels have rollers set at an angle to the axle, allowing each wheel to exert forces in {{c1::multiple directions}}.
Published	11/26/2024	A vehicle with four mecanum wheels can achieve omnidirectional motion by coordinating {{c1::rolling and steering forces}}.
Published	11/26/2024	Mecanum-wheeled robots often operate best indoors on {{c1::smooth floors}}, where they avoid debris interference.
Published	11/26/2024	A robot with omnidirectional mecanum wheels needs a minimum of {{c1::three wheels}} to achieve full mobility.
Published	11/26/2024	Mecanum wheels are ideal for indoor logistics but less suited for outdoor environments due to {{c1::ground conditions}}.
Published	11/26/2024	The control inputs for a simplified unicycle model are typically {{c1::linear velocity}} \( v \) and {{c2::angular velocity}} \( \omega \).
Published	11/26/2024	Nonholonomic systems have constraints that prevent certain motions without violating the {{c1::non-slip assumption}}.
Published	11/26/2024	For car-like robots, the point where wheels intersect is called the {{c1::Instantaneous Center of Rotation (ICR)}}.
Published	11/26/2024	The pose of a robot in its frame of reference is described by the {{c1::generalized coordinates}} \( q = (\theta, x, y) \).
Published	11/26/2024	Differential drive robots turn by creating a difference in speed between the {{c1::left and right wheels}}.
Published	11/26/2024	Omnidirectional wheels allow for movement in multiple directions simultaneously, achieving true {{c1::holonomic control}}.
Published	11/26/2024	In car-like robots, the ability to turn requires {{c1::forward motion}} due to their wheel configuration.
Published	11/26/2024	The kinematic model of a wheeled robot assumes the ground is {{c1::hard and flat}} with no slipping.
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