Dynamic Control of Arm-Type Robots

Dynamic Control of Arm-Type Robots: Motivation. So that the end-effector describes a desired Cartesian trajectories, all joints must track specific joint-space trajectories. So that the end-effector describes a desired joint trajectories, all joints must track specific Cartesian trajectories.

Objective of the dynamic control: Get the joints to track the trajectories defined by the kinematic control as accurately as possible. TRUE. FALSE.

Dynamic control makes use of: -Dynamic control: Multivariables, highly linear, highly coupled and time-varying -Control theory: Analysis and design of controllers. -Dynamic control: One variable, highly non-linear, decoupled and time-varying -Control theory: Analysis and design of controllers. -Dynamic control: Multivariables, highly non-linear, highly coupled and time-varying -Control theory: Analysis and design of controllers. -Dynamic control: One variable, highly non-linear, highly coupled and time-staying -Control theory: Analysis and design of controllers.

Dynamic control is usually carried out in the cartesian coordinate space: cartesian coordinates are controlled. TRUE. FALSE.

Two approaches for dynamic control: Independent control. Independent control: -The whole robot is considered as a multivariable system -All control actions are computed together to control all joint coordinates at once. Independent control: -Each joint is considered as an independent control system -Multiple control action (joint coordinate) and multiple variable to control (motor input ). Independent control: -Each joint is considered as an dependent control system -One control action (motor input) and one variable to control (joint coordinate). Independent control: -Each joint is considered as an independent control system -One control action (motor input) and one variable to control (joint coordinate).

Two approaches for dynamic control: Model-based control. -The whole robot is considered as a single variable system -All control actions are computed together to control all joint coordinates at once. -Each joint is considered as an independent control system -One control action (motor input) and one variable to control (joint coordinate). -The whole robot is considered as a multivariable system -Every control action is computed alone to control all joint coordinates at once. -The whole robot is considered as a multivariable system -All control actions are computed together to control all joint coordinates at once.

Independent Control: Validity. Dynamic model. -Assuming dependent control involves no coupling between joints -It involves considering Inertia and Coriolis matrices can be assumed as diagonal -Assume that the incrementation gearboxes are used in every joint. -Assuming independent control involves coupling between joints -It involves considering Inertia and Coriolis matrices can be assumed as diagonal -Assume that the incrementation gearboxes are used in every joint. -Assuming independent control involves coupling between joints -It involves considering Inertia and Coriolis matrices can not be assumed as diagonal -Assume that the reduction gearboxes are used in every joint. -Assuming independent control involves no coupling between joints -It involves considering Inertia and Coriolis matrices can be assumed as diagonal -Assume that the reduction gearboxes are used in every joint.

If the gear ratio K is high enough, the disturbance torque is negligible when compared to the remaining torques. The independent control is valid and the joint controllers can be designed based on the knowledge of M1 and Cva. The independent control is not valid and the joint controllers can not be designed based on the knowledge of M1 and Cva. The independent control is valid and the joint controllers can be designed based on the knowledge of J1 and Cva. The independent control is valid and the cartesian controllers can be designed based on the knowledge of M1 and Cva.

Independent Control. Nested Control. Two Control loops: OUTER LOOP. -Responsible for maintaining position -Determines the velocity of the joint that minimizes position error. -Responsible for alterning position -Determines the velocity of the joint that minimizes position error. -Responsible for maintaining the velocity -Its reference is determined by the inner loop. -Responsible for maintaining position -Determines the velocity of the joint that maximizes position error.

Independent Control. Nested Control. Two Control loops: INNER LOOP. -Responsible for maintaining the velocity of the joint -Its reference its determined by the outer loop. -Responsible for maintaining the velocity of the joint -Its reference its determined by the outer loop. -Responsible for maintaining position -Determines the velocity of the joint that minimizes position error. -Responsible for maintaining the velocity of the joint -Its reference its determined by the outer loop.

Independent Control. Nested control: INNER LOOP Implementation details. -Time delay: Models the computational time of the velocity control algorithm -Saturation: Models the finite maximum torque to be delivered by the motor. -Time delay: Models the computational time to be delivered by the motor -Saturation: Models the finite maximum torque of the velocity control algorithm.

Independent Control. Nested control: INNER LOOP with a Proportional Controller with unknown disturbances. Small tracking error. Big tracking error.

Independent Control. Nested control: INNER LOOP with Proportional-Integral control to deal with known disturbances. TRUE. FALSE.

Independent Control. Nested control: INNER LOOP with Proportional-Integral control to deal with UNKNOWN disturbances, STRATEGIES. -The integral term can lead to increased overshoot: If you increase Kv, you should reduce Ki -If the joint actuator reaches its limit: integral windup. -The integral term can lead to increased overshoot: If you increase Kv, you should reduce Ki -If the joint actuator doesn't reach its limit: integral windup. -The integral term can lead to increased overshoot: If you increase Ki, you should reduce Kv -If the joint actuator reaches its limit: integral windup. -The integral term can lead to reduced overshoot: If you increase Kv, you should reduce Ki -If the joint actuator reaches its limit: integral windup.

Independent Control. Nested control: INNER LOOP with Torque Feedforward control to deal with known disturbances. TRUE. FALSE.

Independent Control. Nested control: INNER LOOP (velocity) Torque feedforward control TUNING STRATEGY. -The motor torque Km is needed -Predict the disturbance -Then the disturbance can be cancelled out. -The motor torque Km is needed -Predict the disturbance -Then the disturbance can be included.

Independent Control. Nested control. We have. -Inner loop (velocity) -Outer loop (position). -Inner loop (position) -Outer loop (velocity).

Independent Control. Nested Control: Feature summary and strengths: "Inner loop: P or PI controller to generatre a torque so that the actual position tracks the position demand". TRUE. FALSE.

Independent Control. Nested Control: Feature summary and strengths: "Outer loop: P or PI controller to generate the velocity demand so that the actual position tracks the position demand (given by the kinematic control)". TRUE. FALSE.

Independent Control. Nested Control: Feature summary and strengths: "Disturbance torques due to gravity and coupling effects impact the performance of the velocity loop". TRUE. FALSE.

Independent Control. Nested Control: Feature summary and strengths: "Gearing increases the magnitude of disturbance torques by 1/G^2 and the variation in inertica and friction by 1/G. FALSE. TRUE.

Independent Control. Nested Control: Feature summary and strengths: "The inner loop performance can be improved by feedforward of the predictable disturbances". TRUE. FALSE.

Independent Control. Nested Control: Feature summary and strengths: "The outer loop performance can not be improved by feedforward of the desired joint velocity (given by the kinematic control)". TRUE. FALSE.

Independent Control. Nested Control LIMITATIONS: "Feedforward must be introduced to compensate for the gravity disturbance torque". TRUE. FALSE.

Independent Control. Nested Control LIMITATIONS: "Inertia variation and other dynamic coupling forces are explicitly dealt with". TRUE. FALSE.

Independent Control. Nested Control LIMITATIONS: "Feedback controller is responsible for rejecting such terms". TRUE. FALSE.

Independent Control. Nested Control LIMITATIONS: "Controllers must be tuned to optimize the open-loop performance at an average operating point". TRUE. FALSE.

Independent Control. Nested Control LIMITATIONS: "Trade-off between performance and accuracy". TRUE. FALSE.