ECE 470: Introduction to Robotics Homework 4

Question 1.

You are tasked to design the joint control for the manipulator arm analyzed in

Homework 3. Using the control partitioning law, and the formulated dynamics in

Homework 3, fill in the required expression (a)-(d) in the block diagram shown in

Figure 1. (6 Points)

Figure 1.

Question 2.

a) Consider a single-link manipulator arm shown Figure 2.

i) Formulate the dynamic equation factoring coulomb and viscous force acting on the

joint and loading due to gravity. You may assume that viscous and coulomb frictions

result in resisting moment 𝑀𝑣 = 𝑏𝑣𝜃̇ and 𝑀𝑐 = 𝑏𝑐sgn (𝜃̇), respectively. (2 Points)

ii) Draw the control block diagram illustrating the use of control law partitioning for

the non-linearities in the system. (8 Points)

You may assume negligible mass distribution for the link and assumed lumped mass at

the distal time as shown.

b) A DC motor is installed to drive the arm with motor torque 𝜏𝑚 input to a gear

transmission ratio 𝜂. Redraw the control diagram incorporating the dynamics of the

actuator. (4 Points)

Figure 2 (a)-(b).

# Introduction to Robotics Homework 4

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ECE 470: Introduction to Robotics Homework 4

Question 1.

You are tasked to design the joint control for the manipulator arm analyzed in

Homework 3. Using the control partitioning law, and the formulated dynamics in

Homework 3, fill in the required expression (a)-(d) in the block diagram shown in

Figure 1. (6 Points)

Figure 1.

Question 2.

a) Consider a single-link manipulator arm shown Figure 2.

i) Formulate the dynamic equation factoring coulomb and viscous force acting on the

joint and loading due to gravity. You may assume that viscous and coulomb frictions

result in resisting moment 𝑀𝑣 = 𝑏𝑣𝜃̇ and 𝑀𝑐 = 𝑏𝑐sgn (𝜃̇), respectively. (2 Points)

ii) Draw the control block diagram illustrating the use of control law partitioning for

the non-linearities in the system. (8 Points)