Admissible Velocities

Definition

Admissible velocities refer to the set of velocity profiles that a control system can follow while satisfying certain constraints and conditions imposed by the system's dynamics and environment. These velocities are crucial in applications such as control theory and robotics, as they ensure that a system behaves in a stable and feasible manner while navigating through its operational space.

5 Must Know Facts For Your Next Test

1. Admissible velocities must comply with physical constraints, such as maximum speed limits and acceleration rates of the robotic system.
2. In robotics, defining admissible velocities helps to ensure that the motion planning algorithms create feasible paths that can be executed without violating system limitations.
3. Admissible velocities can vary based on the context, such as terrain type or environmental conditions, which can affect a robot's ability to maintain stability and control.
4. In control theory, admissible velocities are often analyzed within the framework of differential inclusions, which generalize the notion of trajectories to account for uncertainties in system dynamics.
5. The concept of admissible velocities is essential in multi-robot systems where coordination among agents must be maintained to prevent collisions and achieve desired goals.

Review Questions

• How do admissible velocities relate to stability in control systems?
  • Admissible velocities are critical for maintaining stability in control systems because they define the range of acceptable speed profiles that the system can follow without becoming unstable. When a system operates within these predefined velocity limits, it can respond effectively to feedback and adapt to changes in its environment. If a system were to exceed these limits, it could lead to loss of control or even failure.
• Discuss how admissible velocities influence motion planning in robotics.
  • In robotics, admissible velocities significantly influence motion planning because they establish the feasible speeds at which a robot can safely navigate through its environment. Motion planning algorithms must take these velocities into account to create paths that not only reach the target location but also adhere to the physical limitations of the robot. This ensures that planned trajectories avoid sharp turns or rapid accelerations that could jeopardize stability or safety.
• Evaluate the impact of environmental factors on determining admissible velocities for robotic systems.
  • Environmental factors play a crucial role in determining admissible velocities for robotic systems as they can affect both the dynamics of motion and safety considerations. For instance, uneven terrain may require lower speeds for stability, while obstacles might necessitate adjustments to velocity profiles for safe navigation. Evaluating these environmental impacts allows robotic systems to adapt their operational parameters dynamically, ensuring efficient performance while minimizing risks associated with unexpected conditions.

Related terms

Control Theory: A branch of engineering and mathematics that deals with the behavior of dynamical systems with inputs, and how their behavior is modified by feedback.

Robot Kinematics: The study of the motion of robots without considering the forces that cause this motion, focusing on position, velocity, and acceleration.

Path Planning: The process of determining a route for a robot or vehicle to follow in order to reach a destination while avoiding obstacles and adhering to constraints.