Intelligent Systems for Robotics (AL-604 (C)) - Unit 1 Short Notes

UNIT 1: FUNDAMENTALS OF INTELLIGENT ROBOTIC SYSTEMS

1.1 Introduction to Robotics

Robotics is the science and technology of designing, constructing, and operating intelligent machines (robots) that can perform tasks autonomously or semi-autonomously.

Basic Aspects of Robotics (Sense-Plan-Act Cycle):

1. Perception (Sense): Using sensors (vision, force, proximity) to gather environmental data.

2. Cognition (Plan): Processing sensor data, reasoning, and planning actions using AI algorithms.

3. Action (Act): Executing planned motions via actuators (motors, hydraulics) through the robot's kinematic chain.

[!TIP] Exam Focus: Be prepared to define robotics and elaborate on the Sense-Plan-Act paradigm with examples (e.g., a robot arm picking an object: vision senses object, AI plans path, motors act).

1.2 Robot Programming Methods

Problems Peculiar to Robot Programming Languages:

• Lack of Sensory Integration: Difficulty in incorporating real-time sensor feedback (e.g., force, vision) into program flow.

• Uncertainty Handling: Challenges in programming for unstructured, dynamic environments.

• Complexity of Motion: Describing smooth, collision-free trajectories for multi-DOF arms is non-trivial.

• Hardware Dependence: Programs often tied to specific robot controllers and kinematics.

1.3 AI in Robotics & Intelligent Agents

Need for AI in Robotics:

To move beyond pre-programmed, repetitive actions to adaptive, intelligent behavior in uncertain environments (e.g., autonomous navigation, object recognition, decision-making under partial information).

Major Types of Intelligent Agents (in order of increasing capability):

1. Simple Reflex Agents: Act based on current percept (condition-action rules). No internal state.

2. Model-Based Reflex Agents: Maintain internal world model (state) to track unobserved aspects.

3. Goal-Based Agents: Incorporate goals and use search/planning to achieve them.

4. Utility-Based Agents: Use a utility function to evaluate desirability of states, enabling trade-offs in uncertain environments.

[!TIP] Common Pitfall: Do not confuse agents with simple programs. Highlight the autonomy, percept, action, and internal state/model aspects.

1.4 Game Playing Programs (AI)

Major Components:

• State Representation: How the game board/situation is stored (e.g., matrix, graph).

• Operators/Actions: Legal moves that transform one state to another.

• Terminal Test: Checks if a state is a win/loss/draw.

• Evaluation Function (Heuristic): f(s) estimates the "goodness" of a non-terminal state for the MAX player.

• Search Algorithm: Explores the game tree (e.g., Minimax, Alpha-Beta Pruning).

Basic Strategy (Minimax Principle):

The algorithm assumes both players play optimally. MAX (our agent) chooses moves to maximize its guaranteed payoff, while MIN (opponent) chooses moves to minimize MAX's payoff.

$$ \text{Minimax}(s) = \begin{cases} \text{Utility}(s) & \text{if terminal}(s) \\ \max_{a} \min_{a'} \text{Minimax}(\text{Result}(s,a)) & \text{if MAX's turn} \\ \min_{a} \max_{a'} \text{Minimax}(\text{Result}(s,a)) & \text{if MIN's turn} \end{cases} $$

[!TIP] Exam Tip: Always draw a small game tree (depth 2 or 3) to illustrate minimax backing up values. Mention Alpha-Beta pruning as an optimization to reduce node evaluations.

1.5 Fundamentals of Robot Kinematics

Kinematics: Study of motion without considering forces. Deals with position, velocity, acceleration.

Key Representations:

• Forward Kinematics (FK): Given joint variables $$\displaystyle \theta_1, \theta_2, ..., \theta_n $$, compute end-effector pose (position & orientation) $[X, Y, Z, \phi, \theta, \psi]$.

• Inverse Kinematics (IK): Given desired end-effector pose, compute required joint variables. Often has multiple solutions or no solution.

Standard Method: Denavit-Hartenberg (D-H) Convention

Assigns a coordinate frame to each link. Four parameters per joint:

• $$\displaystyle \theta_i $$: Joint angle (rotation about $$\displaystyle z_{i-1} $$)

• $$\displaystyle d_i $$: Link offset (translation along $$\displaystyle z_{i-1} $$)

• $$\displaystyle a_i $$: Link length (translation along $$\displaystyle x_i $$)

• $$\displaystyle \alpha_i $$: Link twist (rotation about $$\displaystyle x_i $$)

Homogeneous Transformation Matrix:

$$ ^{i-1}T_i = Rot(z,\theta_i) \cdot Trans(z,d_i) \cdot Trans(x,a_i) \cdot Rot(x,\alpha_i) $$

$$ = \begin{bmatrix} \cos\theta_i & -\sin\theta_i\cos\alpha_i & \sin\theta_i\sin\alpha_i & a_i\cos\theta_i \\ \sin\theta_i & \cos\theta_i\cos\alpha_i & -\cos\theta_i\sin\alpha_i & a_i\sin\theta_i \\ 0 & \sin\alpha_i & \cos\alpha_i & d_i \\ 0 & 0 & 0 & 1 \end{bmatrix} $$

Forward Kinematics: $$\displaystyle ^0T_n = ^0T_1 \cdot ^1T_2 \cdot ... \cdot ^{n-1}T_n $$

[!DIAGRAM] Search: "Denavit-Hartenberg parameters robot arm diagram" for visual frame assignment.

Reverse Kinematics Example (2-DOF Planar Arm):

Given $(x, y)$:

$$ \theta_2 = \cos^{-1}\left( \frac{x^2 + y^2 - l_1^2 - l_2^2}{2 l_1 l_2} \right) \quad (\text{elbow up/down}) $$

$$ \theta_1 = \tan^{-1}(y/x) - \tan^{-1}\left( \frac{l_2 \sin\theta_2}{l_1 + l_2 \cos\theta_2} \right) $$

1.6 Coordinate Transformations & Rotations

Line Coordinates & Hayati-Roberts Coordinates: Alternative representations for tool orientation, particularly useful for wrist-partitioned robots (separate position and orientation). Hayati-Roberts uses three angles ($\theta, \phi, \psi$) to describe the orientation of the tool frame relative to the wrist frame, simplifying IK for spherical wrists.

Composition of Rotations about Moving Axes:

Rotations about body-fixed (moving) axes are not commutative. The final orientation depends on the order. Represented by multiplying individual rotation matrices in reverse order of application.

For rotations $$\displaystyle R_x(\alpha) $$, $$\displaystyle R_y(\beta) $$, $$\displaystyle R_z(\gamma) $$ about moving axes:

$$ R = R_z(\gamma) \cdot R_y(\beta) \cdot R_x(\alpha) $$

[!TIP] Common Error: Students often confuse fixed-axis (extrinsic) vs. moving-axis (intrinsic) rotations. For moving axes, apply rotations in reverse order when multiplying matrices.

1.7 Kinematic Chain Topologies

• Serial Chain: Links connected end-to-end (e.g., typical 6-DOF industrial arm). Advantage: Large workspace. Disadvantage: Low stiffness, cumulative errors.

• Parallel Chain: End-effector connected to base via multiple independent chains (e.g., Stewart platform). Advantage: High stiffness, accuracy. Disadvantage: Limited workspace, complex IK.

• Hybrid (Serial-Parallel): Combines both (e.g., a serial arm with a parallel wrist).

1.8 Dynamics & Decoupling

Dynamics: Study of motion with forces/torques. Relates joint torques $\tau$ to motion (accelerations $\ddot{q}$).

General equation:

$$ \tau = M(q)\ddot{q} + C(q,\dot{q})\dot{q} + G(q) + F(\dot{q}) $$

where $M$ = inertia matrix, $C$ = Coriolis/centrifugal, $G$ = gravity, $F$ = friction.

Decoupling about Center of Mass:

For a rigid body, the dynamics can be separated into:

1. Translational Motion of the center of mass: $$\displaystyle F = m \cdot a_{cm} $$

2. Rotational Motion about the center of mass: $$\displaystyle \tau_{cm} = I_{cm} \cdot \alpha + \omega \times (I_{cm} \omega) $$

This simplifies the equations of motion for each link in a kinematic chain.

1.9 Accuracy & Repeatability

[!TIP] Crucial Distinction: A robot can be highly repeatable but inaccurate (consistently off by the same error). Most industrial tasks require high repeatability.

1.10 Robot Components & Architecture

Joints & Links:

• Links: Rigid bodies connecting joints.

• Joints: Provide relative motion. Main types:

  • Revolute (R): Rotational motion (1 DOF).

  • Prismatic (P): Linear sliding motion (1 DOF).

  • A robot's DOF = number of independent joints.

Robotic System Architecture:

1. Mechanical Structure: Links, joints, end-effector.

2. Sensors: Provide feedback (position, force, vision).

3. Controller: CPU + control algorithms (PID, computed torque) executing the plan.

4. Power Source & Drives: Motors/actuators and their drivers.

5. User Interface: Teach pendant, off-line programming station.

1.11 Drive Systems Comparison

1.12 Structure of Intelligent Agents (PEAS Framework)

Define an agent by its:

• Performance Measure: What is the goal? (e.g., "minimize task time," "maximize safety").

• Environment: Where does it operate? (e.g., static/dynamic, discrete/continuous, single/multi-agent).

• Actuators: How does it act? (e.g., robot joints, gripper).

• Sensors: What does it perceive? (e.g., cameras, lidar, joint encoders).

Agent Function: f: P^* \rightarrow A maps any percept history to an action. Agent Program: Implementation of the agent function.

[!TIP] Exam Application: For any robotics question, frame the answer using PEAS. E.g., for a self-driving car: Performance = safety, efficiency; Environment = roads, traffic; Actuators = steering, throttle, brakes; Sensors = cameras, radar, GPS.