Intelligent Systems for Robotics (AL-604 (C)) - Unit 2 Short Notes

Unit 2: Fundamentals of Intelligent Robotics

I. Introduction to Robotics and AI Integration

Robotics is the science and technology of designing, building, and applying robots—programmable machines that can perform tasks autonomously or semi-autonomously.

Basic Aspects of Robotics:

• Perception: Sensing the environment (vision, force, proximity).

• Cognition/Decision-Making: Processing information and planning actions.

• Action: Executing motions via actuators (motors, cylinders).

• Integration: Combining hardware (mechanical) and software (intelligence).

Need for AI in Robotics:

• To handle uncertain, dynamic, and unstructured environments.

• For autonomous decision-making without explicit pre-programming for every scenario.

• To enable learning, adaptation, and reasoning from sensory data.

• For human-robot interaction and collaborative tasks.

Major Types of Intelligent Agents in Robotics:

Structure of Agents:

• Architecture: Hardware/software framework (sensors → processing → actuators).

• Program: Implements the agent function (mapping percepts to actions).

• [!TIP] Exam Focus: Be prepared to draw a block diagram of a generic agent structure and label its components (percept, environment, agent function, actuators).

II. Robot Programming Paradigms

Various Programming Methods:

1. Lead-by-the-Nose / Teaching Pendant: Manual guidance; points recorded.

2. Offline Programming (OLP): Programming in a simulated 3D environment.

3. Textual Programming Languages: Specialized languages (e.g., VAL, KRL, RAPID).

4. Graphical/Interactive Programming: Drag-and-drop blocks, flowcharts.

5. Learning from Demonstration (LfD): Robot learns by observing human task execution.

6. Motion Scripting: Using predefined motion primitives (point-to-point, linear, circular).

Problems Peculiar to Robot Programming Languages:

• Real-time Constraints: Must guarantee timing for motion control loops.

• Concurrency: Handling multiple processes (motion, I/O, sensing) simultaneously.

• Spatial Reasoning: Native support for 3D geometry, transformations, and kinematics.

• Sensor Integration: Complex syntax for processing asynchronous sensor data.

• Safety: Built-in mechanisms to prevent collisions or unsafe motions.

• Hardware Dependence: Often proprietary to specific robot manufacturers.

• [!TIP] Common Pitfall: Do not confuse general-purpose programming issues (e.g., memory leaks) with robot-specific issues like kinematic singularity handling or real-time interrupt service routines.

III. AI Techniques for Robotic Decision-Making

Game Playing Programs in AI:

Major Components:

1. State Representation: How the game board/situation is stored (e.g., 8x8 grid for chess).

2. Move Generator: Function to produce all legal moves from a state.

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

4. Evaluation Function (Heuristic): Estimates the "goodness" of a non-terminal state. Crucial for non-trivial games.

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

Basic Strategy in Game Playing (Minimax Principle):

• Assumes a two-player, zero-sum, perfect-information game.

• The AI (MAX) tries to maximize its minimum guaranteed payoff, assuming the opponent (MIN) plays optimally to minimize MAX's score.

• Search Tree: Alternating MAX and MIN levels.

• Formula (for a MAX node): value(s) = max_{a ∈ moves(s)} min_{s' ∈ result(a)} value(s')

• Alpha-Beta Pruning: Optimizes Minimax by pruning branches that cannot affect the final decision.

  • α (alpha): Best (highest) value that MAX can guarantee at that level or above.

  • β (beta): Best (lowest) value that MIN can guarantee at that level or above.

  • Prune when α ≥ β.

Role of AI in Autonomous Decision-Making:

• Provides planning (STRIPS, PDDL), reasoning under uncertainty (Bayesian networks, Markov Decision Processes), and learning (reinforcement learning) capabilities.

• Enables robots to move from reactive (stimulus-response) to proactive (goal-directed, deliberative) behavior.

IV. Motion Planning and Trajectory Generation

Trajectory Planning:

• Definition: The problem of finding a time-parameterized path q(t) (joint space) or x(t) (Cartesian space) that satisfies:

  1. Kinematic constraints: Velocity v_max, acceleration a_max limits.

  2. Dynamic constraints: Torque/force limits (often decoupled in simpler planning).

  3. Obstacle avoidance: Entire trajectory must be collision-free.

  4. Boundary conditions: Start/end at specified (position, velocity) states.

• Output: A smooth, feasible motion profile for the controller to follow.

Path Planning Methodologies:

[!TIP] Distinguish Clearly: Path = geometric curve in space (no time). Trajectory = path + timing specification (time-parameterized). Motion Plan = complete solution (often a trajectory) satisfying all constraints.

V. Robotic Kinematics

Robot Kinematics Representations:

• Forward Kinematics (FK): Given joint variables q = [q1, q2, ..., qn]^T, compute end-effector pose T ∈ SE(3).

  • T = f(q) (nonlinear mapping).

• Inverse Kinematics (IK): Given desired end-effector pose T_des, find joint variables q such that f(q) = T_des.

  • May have multiple solutions, no solution, or infinite solutions (redundancy).

• Denavit-Hartenberg (D-H) Convention: Standard method to assign coordinate frames and derive FK. Uses 4 parameters per link (θ, d, a, α). Transformation: A_i = Rot_z(θ_i) * Trans_z(d_i) * Trans_x(a_i) * Rot_x(α_i).

  • T_0^n = A_1 * A_2 * ... * A_n

Reverse Kinematics of Manipulators:

Two DOF Planar Manipulator (Revolute-Revolute):

• Structure: Two links l1, l2 in a plane.

• FK: x = l1*cos(q1) + l2*cos(q1+q2), y = l1*sin(q1) + l2*sin(q1+q2)

• IK Solution (Elbow-up/down):

  q2 = atan2(±√(1-c²), c) where c = (x² + y² - l1² - l2²)/(2*l1*l2)

  q1 = atan2(y, x) - atan2(l2*sin(q2), l1 + l2*cos(q2))

  • Two solutions from ± in q2 (elbow-up, elbow-down).

Three DOF Manipulator (e.g., Spherical Wrist):

• Often decoupled: Position (first 3 joints) and Orientation (last 3 joints, spherical wrist).

• IK for Position: Solve first 3 joints to place wrist center (x_c, y_c, z_c).

  • For RRR (anthropomorphic arm): Similar to 2-DOF but in 3D, leads to quadratic equation.

  • For RPR or PRR: Different geometric solutions.

• IK for Orientation: Once wrist center is fixed, last 3 joints (usually roll, pitch, yaw) solve a simple Euler angle problem from the desired rotation matrix R_des.

• [!TIP] Key Insight: For many industrial arms (6-DOF with spherical wrist), IK decouples into a 3-DOF position problem and a 3-DOF orientation problem, drastically simplifying solution.

Coordinate Transformation Systems:

Composition of Rotations About Moving Axes:

• Moving-Axis (Intrinsic) Rotations: Rotations are applied relative to the current, rotated coordinate system.

  • Sequence: R = R_z(θ1) * R_y(θ2) * R_x(θ3) (ZYZ Euler angles are common in robotics).

  • Critical: Order matters. Each rotation is about the new axis after previous rotations.

• Fixed-Axis (Extrinsic) Rotations: Rotations are about the original, fixed base frame.

  • Sequence: R = R_x(θ3) * R_y(θ2) * R_z(θ1) (reverse order of intrinsic for same final orientation).

• [!TIP] Common Error: Confusing intrinsic (moving) vs. extrinsic (fixed) rotation sequences. In D-H, transformations are extrinsic (each A_i transforms from frame i-1 to i about frame i-1's axes). Euler angles for orientation are often intrinsic.

Kinematic Chain Topologies:

• Serial Chain: Single chain from base to end-effector (e.g., typical manipulator arm). Advantage: Large workspace. Disadvantage: Low stiffness, cumulative errors.

• Parallel Chain: Multiple chains from base to a moving platform (e.g., Stewart platform). Advantage: High stiffness, precision, load capacity. Disadvantage: Small workspace, complex IK.

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

VI. Robotic Dynamics

Rigid Body Dynamics:

• Models the relationship between forces/torques and motion (acceleration).

• Two primary formulations:

  1. Newton-Euler: Force/torque balance on each link (recursive, efficient for simulation/control).

  2. Lagrangian: Energy-based (L = T - V), yields equations of motion: τ = M(q)q̈ + C(q, q̇)q̇ + G(q)

     • M(q): Inertia matrix (symmetric, positive definite).

     • C(q, q̇)q̇: Coriolis and centrifugal terms.

     • G(q): Gravity vector.

     • τ: Joint torques/forces.

Decoupling of Rigid Body Dynamics about Center of Mass:

• For a free-floating rigid body (not fixed to a joint), Newton's 2nd law and Euler's equation can be separated:

  • Translational Motion: F_ext = m * a_cm (Force = mass * acceleration of center of mass).

  • Rotational Motion: τ_ext = I_cm * α + ω × (I_cm * ω) (Torque about CM = rate of change of angular momentum about CM).

• Key Point: The dynamics of translation and rotation decouple when referenced to the center of mass (CM). This simplifies analysis of free bodies (e.g., a thrown object, a satellite).

• For a manipulator arm, dynamics are coupled (terms in M, C link all joints), but the principle of separating CM motion is foundational.

VII. Robotic System Performance Metrics

Accuracy:

• Definition: Ability of the robot's end-effector to reach a commanded position.

• Measure: Absolute error between desired position (x_d, y_d, z_d) and the mean of actual achieved positions (x̄, ȳ, z̄).

  Accuracy = √[(x_d - x̄)² + (y_d - ȳ)² + (z_d - z̄)²]

• Factors: Kinematic model errors, calibration, gear backlash, thermal drift.

• [!TIP] Analogy: Accuracy is about correctness (hitting the bullseye).

Repeatability:

• Definition: Ability of the robot to return to the same taught position multiple times.

• Measure: Standard deviation (σ) or maximum spread (ball diameter) of actual positions when repeatedly commanded to the same point.

  Repeatability (σ) = √[Σ(x_i - x̄)²/(N-1)] (applied to each axis and combined).

• Factors: Resolution of encoders, control loop jitter, mechanical backlash, friction.

• [!TIP] Analogy: Repeatability is about consistency/precision (clustering of shots, even if off-target).

• Critical Distinction: A robot can be repeatable but not accurate (consistent error). Accuracy requires both good repeatability and correct calibration.

VIII. Robotic Mechanical Structure

Robot Joints and Links:

• Link (L_i): Rigid body connecting two joints. Denoted by i.

• Joint (J_i): The movable connection between link i-1 and link i. Provides degree-of-freedom (DOF).

• Kinematic Chain: Sequence J_1 - L_1 - J_2 - L_2 - ... - J_n - L_n (end-effector).

Types and Classifications of Joints:

1. By Motion Type:

   • Revolute (R): Single-DOF rotary motion (like a hinge). Most common.

   • Prismatic (P): Single-DOF linear sliding motion.

   • Less common: Spherical, Universal, Cylindrical.

2. By Power Transmission:

   • Direct Drive: Motor directly coupled to joint (no gears). High bandwidth, no backlash.

   • Geared: Uses gears (harmonic, cycloidal, planetary). High torque density, but introduces backlash, friction, compliance.

Link Design Considerations:

• Stiffness: Minimize deformation under load (high EI for beams, use closed sections).

• Strength: Withstand static/dynamic loads without yielding or fatigue failure.

• Weight: Inertia directly affects actuator size and control performance. Use lightweight materials (aluminum, composites).

• Kinematic Compatibility: Must allow required range of motion without self-collision.

• Routing: Internal passages for wiring, hydraulics, and cooling.

• Manufacturability & Cost: Balance performance with production feasibility.

IX. Robotic System Architecture

Architecture of Robotic Systems:

Refers to the organizational structure of hardware and software components.

Common Control Architectures:

1. Hierarchical (Deliberative):

   • Structure: Pyramid of levels (Strategic → Tactical → Executive → Servo).

   • Flow: Top-down planning, bottom-up sensing. Each level operates at a different rate and abstraction.

   • Pros: Systematic, good for complex, known tasks.

   • Cons: Slow, brittle in dynamic environments.

2. Reactive (Subsumption):

   • Structure: Network of parallel, simple behavior modules (e.g., "avoid-obstacle", "wander").

   • Flow: Sensors directly trigger actions. Higher-priority behaviors can suppress lower ones.

   • Pros: Fast, robust, simple.

   • Cons: Hard to design complex, goal-directed sequences.

3. Hybrid (Three-Layer):

   • Common Modern Architecture:

     • Deliberative Layer: High-level planning, scheduling (slow, ~1 Hz).

     • Executive Layer: Sequencer, state machine, monitors (medium, ~10-100 Hz).

     • Reactive Layer: Low-level servo control, reflex loops (fast, >100 Hz).

   • Pros: Combines responsiveness with goal-directedness.

   • Cons: Integration complexity.

System Component Integration:

• Sensors → Perception Module → World Model → Planner → Controller → Actuators → Robot.

• Middleware (e.g., ROS) often used for communication between decoupled modules (nodes).

X. Robotic Actuation and Drive Systems

Comparative Analysis of Drive System Types:

[!TIP] Rule of Thumb: Electric dominates modern precision robotics. Hydraulic for extreme force/size. Pneumatic for simple, fast, low-cost linear motion where stiffness/precision isn't critical.