Robotics (IT-802 (C)) - Important Questions

Explain the working principles of P, PD and PID controllers used for position control of a robotic joint. Write the time-domain expression of a PID controller and discuss qualitatively how $K_p$, $K_i$ and $K_d$ affect steady-state error, rise time, overshoot and stability.

Derive the closed-loop transfer function for a unity feedback system with plant $G(s)$ and a PID controller $C(s)=K_p+\frac{K_i}{s}+K_d s$. Show the characteristic equation and explain how each term $K_p$, $K_i$, $K_d$ modifies the poles of the closed-loop system.

Explain the Ziegler–Nichols tuning procedure based on the ultimate gain $K_u$ and ultimate period $T_u$. Using the plant $G(s)=\frac{1}{s\left\(s+2\right\)}$, outline the steps to obtain $K_u$ and $T_u$ and compute the PID parameters $K_p$, $K_i$ and $K_d$ as per the Ziegler–Nichols rules. State any assumptions you make.

For the robot manipulator dynamics $M(q)\ddot q + C(q,\dot q)\dot q + G(q)=\tau$, derive the computed-torque (feedback linearization) control law that yields a linear error dynamics. Show the control law in the form $\tau=M(q) v + C(q,\dot q)\dot q + G(q)$ and specify a typical choice of $v$ using PD terms for tracking. Briefly compare this approach with sliding mode control for robustness to model uncertainties.

Compare electric, hydraulic and pneumatic actuators for robotic joints. For each type discuss: typical power density, controllability, compliance, maintenance issues and typical application scenarios in robotics.

A rotary robot joint carries a payload of mass $m$ at a distance $l$ from the joint axis and the link has moment of inertia $I_{link}$ about the joint. Derive expressions for the required actuator torque $\tau$ to achieve a desired angular acceleration $\alpha$ at joint angle $\theta$, considering gravitational torque. Use $I_{a}=m l^{2}+I_{link}$ to denote the reflected inertia. Include the expression for the continuous power required if the joint rotates at angular speed $\omega$. Show all formulas explicitly.

Explain the working principles and typical uses of the following transmission mechanisms in robotic manipulators: spur gear trains, planetary gears, timing belts and harmonic drives. Derive the basic relation between speed and gear teeth for a simple two-gear pair and write the relation expressing torque multiplication considering an ideal (lossless) gear pair.

A two-gear reduction has driving gear with $N_1=20$ teeth and driven gear with $N_2=60$ teeth. The motor shaft provides $\tau_{in}=0.5\ \mathrm{Nm}$ at $\omega_{in}=3000\ \mathrm{rpm}$ and the gearbox efficiency is 95%. Compute: (a) gear ratio, (b) output speed $\omega_{out}$ in rpm, and (c) output torque $\tau_{out}$ accounting for efficiency. Show calculations and formulas used.

Discuss the effects of backlash, compliance and transmission stiffness on position control accuracy and stability of robotic manipulators. Describe engineering measures to minimise their impact (for example: preloading, direct-drive, harmonic drives, torsional springs, control compensation) and explain how these choices trade off with cost and complexity.