Trajectory Planning

Which type of trajectory planning is best suited for robots with complex kinematic structures, where it is difficult to find an analytical solution for joint-space trajectories?

• Linear trajectory planning

• Cartesian-space trajectory planning

• Joint-space trajectory planning with cubic polynomials

• Joint-space trajectory planning with fifth-order polynomials

In Cartesian-space trajectory planning, what is the primary advantage of using cubic polynomials for trajectory generation?

• Smooth trajectories with continuous velocity and acceleration profiles

• Minimized computation and control effort

• Faster execution of trajectories

• Improved accuracy in reaching the desired end-effector pose

What is the key drawback of using fifth-order polynomial trajectories in joint-space trajectory planning?

• They result in jerky and discontinuous motion

• They require a high level of computational resources

• They have limited compatibility with robot controllers

• They are unsuitable for reaching complex target poses

Linear trajectory functions are typically used for:

• Generating trajectories with constant velocity in Cartesian space

• Producing complex joint-space trajectories for industrial robots

• Ensuring smoother joint motion with high-order polynomials

• Minimizing the time to reach the desired Cartesian pose

Which trajectory planning approach is most suitable when the primary objective is to minimize energy consumption during robot motion?

• Fifth-order polynomial trajectories in joint-space

• Linear trajectory functions in Cartesian space

• Joint-space trajectory planning with cubic polynomials

• Cartesian-space trajectory planning with velocity profiles

In joint-space trajectory planning with cubic polynomials, what is the significance of using a "blend radius"?

• It determines the maximum robot joint speed

• It specifies the time required to reach the target pose

• It controls the smooth transition between path segments

• It defines the maximum allowable acceleration during motion

Which type of trajectory planning is more suitable for applications requiring precise control over individual joint positions, such as robotic arms in manufacturing?

• Cartesian-space trajectory planning with cubic polynomials

• Joint-space trajectory planning with linear trajectory functions

• Fifth-order polynomial trajectories in joint-space

• Cartesian-space trajectory planning with high-order polynomials

In the context of trajectory planning, what does the term "Jerk" refer to?

• A sudden change in velocity

• The derivative of acceleration

• A type of robot joint

• The time derivative of position

When using trajectory optimization techniques, which factor is usually considered as a cost function to be minimized?

• Joint velocities

• Robot's maximum speed

• Energy consumption

• End-effector orientation

Which mathematical optimization technique is commonly applied to find optimal trajectories for robot motion in complex environments?

• Linear programming

• Quadratic programming

• Differential equations

• Fourier analysis