Locomotion

Week 1 • CMPSC 304 Robotic Agents

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Today's Agenda

  • What is actuation?
  • Locomotion vs. manipulation
  • Static vs. dynamic stability
  • Degrees of Freedom (DoF)
  • Wheel types and kinematics

Actuation: Making Robots Move

Actuation = The robot's ability to move and interact with the world

Two key types:

  • Locomotion: Moving the robot itself
  • Manipulation: Moving objects in the environment

The Duality of Movement

Both use the same principle:

  • Motors exert forces on the environment
  • Locomotion: Forces on ground/water/air → robot moves
  • Manipulation: Forces on objects → objects move
Example: Insect legs do both!

Locomotion Methods

Rolling Walking Running Jumping
Swimming Flying Crawling Sliding
Key Question: Which mechanism is best for your application?

Trade-offs: energy efficiency, terrain, speed, stability, cost

Energy Efficiency

Power consumption vs speed
Rolling provides best energy-to-speed ratio
Railway wheels ~10× more efficient than walking

But Wheels Have Limits

Great For:

  • ✓ Roads
  • ✓ Warehouses
  • ✓ Flat floors

Poor For:

  • ✗ Forests
  • ✗ Mountains
  • ✗ Rough terrain
Legs excel where wheels fail!

This is why evolution never created wheeled animals

Stability Types

Static

Won't fall when not moving

  • ✓ Stable at rest
  • ✓ Slower movements
  • ✓ Simpler control

Dynamic

Requires constant motion

  • ✓ Faster, agile
  • ✗ Complex control
  • ✗ Always actuating

Stability Principle

Stability examples
Center of mass must stay within ground-contact polygon
  • Left: Static (stable at rest)
  • Middle: Dynamic (must keep moving)
  • Right: Both modes possible

Real-World Examples

Six Legs

(Insects, hexapods)

  • Statically stable walking
  • Move 3 legs at a time
  • Triangle always supports

Four Legs

(Dogs, quadruped robots)

  • Walking = static
  • Running = dynamic
  • Switch between modes

Degrees of Freedom (DoF)

DoF = Independent ways a system can move

Two types to distinguish:

  1. Cartesian DoF: Positions/orientations in space
    (Maximum 6 in 3D space)
  2. Mechanical DoF: Number of actuated joints
    (Depends on robot design)

Cartesian DoF (3D Space)

Pitch, yaw, and roll
Translation (3):
  • Forward/back
  • Left/right
  • Up/down
Rotation (3):
  • Pitch
  • Yaw
  • Roll

Wheel Types & DoF

Wheel types

Different wheel types enable different mobility

Standard Wheel (2 DoF)

Two degrees of freedom:

  1. Rotation around the wheel axle
  2. Rotation around ground contact point
Constraint: Can only roll in one direction
Cannot move sideways (would require skidding)

Example: Bicycle wheel, car wheel

Caster Wheel (3 DoF)

Three degrees of freedom:

  1. Rotation around the wheel axle
  2. Rotation around ground contact
  3. Rotation around the caster axis
Can reorient to roll in any direction!

Example: Shopping cart, office chair

Swedish/Mecanum Wheel (3 DoF)

Three degrees of freedom:

  1. Rotation around main wheel axle
  2. Rotation around ground contact
  3. Rotation around roller axles
Rollers on circumference allow sideways motion
Result: True omnidirectional movement!

Kinematic Constraints

3-DoF wheels = Free movement on a plane
2-DoF wheels = Constrained movement
But constrained ≠ unreachable!
  • A car can parallel park
  • Requires multiple maneuvers
  • Like a knight on a chessboard

Mobile Robot DoF on a Plane

A plane has 3 Cartesian DoF:

  • X position (horizontal)
  • Y position (vertical)
  • Orientation (angle θ)
Robots without 3-DoF wheels have kinematic constraints

May need multiple moves to reach certain poses

Manipulator Arms: Mechanical DoF

Each actuated joint typically adds 1 mechanical DoF

On a plane (2D workspace):

  • Up/down position
  • Left/right position
  • End-effector orientation

3 Cartesian DoF needed → Need ≥3 joints

Joint Types

Revolute (Rotary)

  • Most common
  • Rotates around an axis
  • Example: Elbow, shoulder

Prismatic (Linear)

  • Extends and contracts
  • Slides along an axis
  • Example: Telescope, piston

Design Trade-offs

Choosing kinematics involves balancing:

  • Mechanical complexity
  • Maneuverability
  • Precision
  • Cost
  • Ease of control
Example: Differential drive vs. car steering
• Differential: cheap, maneuverable, hard to drive straight
• Car: expensive, precise, hard to parallel park

Real Robot: Differential Drive

Configuration:

  • Two powered wheels on shared axis
  • One (or two) caster wheels for support

Advantages

  • Very maneuverable
  • Simple control
  • Low cost

Challenge

  • Hard to drive straight
  • Needs matched motors
  • Wheel wear issues

Key Takeaways

  1. Actuation enables locomotion and manipulation
  2. Stability can be static (at rest) or dynamic (requires motion)
  3. DoF describes what movements are possible
  4. Wheel type determines mobility constraints
  5. Design choices involve complex trade-offs

Before Next Class

Building your wheeled robot!

Think about:

  • What DoF does your robot need?
  • Static or dynamic stability?
  • Which wheel configuration?
  • What trade-offs will you make?

Questions?

Next: Continue Project 1 (Wheeled Robot)
  • Submit components list and team contract
  • Finish Design
Next Week:
  • Mechanical build
  • Wiring and power
  • Basic control

Readings: IAR Chapters 2 & 6