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Autonomous Mobile Manipulation

Wheeled Robot Kinematics

C. Papachristos

Robotic Workers (RoboWork) Lab

University of Nevada, Reno

CS-791

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Kinematics & Dynamics

  • Kinematics:
    • Provide motion of the robot without consideration of forces or torques producing the motion

Important to consider for animation, navigation control, guidance, robot design, etc.

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  • Dynamics:
    • Describe relationship between forces and motions

Important to consider for simulation, optimal control, robot design etc.

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Kinematics – Holonomic Constraint

 

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Kinematics – Non-holonomically Constrained

 

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Kinematics – Nonholonomic Robot

Non-Holonomic ground robot

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  • Differential equations not exactly integrable to the final configuration
    • Position integrated over time (and unbounded in the general case), depends on path taken

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  • Measure of traveled distance of each wheel is not sufficient to calculate the final position of the robot; One has also to know how this movement was executed as a function of time
    • E.g. in contrast to an actuator arm
      • (open kinematic chain)

 

 

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Kinematics – Nonholonomic Robot

Forward and Inverse Kinematics

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  • Forward Kinematics
    • Transformation from joint space to configuration space

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  • Inverse Kinematics
    • Transformation from configuration space to joint space
    • Required for motion control

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  • Due to non-holonomic constraints in mobile robotics, we deal with Differential (Inverse) Kinematics
    • Transformation between velocities instead of positions
    • Differential kinematic model has the following form:

Non-Integrable Robot Model

 

 

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Wheeled Robots

 

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Wheel Types

Basic

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a) Standard wheel

  • Rotation around the (motorized) wheel axle and the contact point

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b) Orientable wheel: Centered & Castor (off-center)

  • Rotation around the wheel axle, the contact point and the castor axle

 

 

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Wheel Types

Advanced

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c) “Mecanum” / Swedish wheel

  • Rotation around the (motorized) wheel axle, around the rollers and around the contact point

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d) Ball wheel on spherical joint

  • Suspension technically not solved

 

 

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Omnidirectional Wheeled Vehicles

“Mecanum”-wheeled Omnidirectional robot

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Movement on the plane has 3 DoF

  • Thus only three wheels can be independently controlled
  • Also possible to arrange 3 such wheels in a triangle

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Kinematic Constraints

Assumptions

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We express kinematic constraints w.r.t. motion constraints individual wheels

  • Combine wheel motions to derive whole body motion

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  • Rigid wheels, rigid chassis
  • Wheel plane remains vertical, motion is on horizontal plane
  • Steering axles orthogonal to motion plane (ground)

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  • Single point of contact of wheel to the motion plane (ground)
    • The Instantaneous Contact Point

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  • No sliding motion at the Instantaneous Contact Point
    • No lateral motion of the wheel

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  • Pure rolling motion at the Instantaneous Contact Point, without slippage
    • Entire body motion “matched” in opposite by the wheel’s Instantaneous Contact Point velocity

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Kinematic Constraints

Steerable Standard Wheel

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Kinematic Constraints

Steerable Standard Wheel

 

 

Rolling Constraint

Sliding Constraint

 

 

 

and

Where:

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Kinematic Constraints

Steerable Castor Wheel

Longitudinal Rolling Constraint

Lateral (Rolling) Constraint

 

and

Where:

 

 

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Kinematic Constraints

“Mecanum” (Swedish) Wheel

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Kinematic Constraints

“Mecanum” (Swedish) Wheel

 

 

Longitudinal Rolling Constraint

Lateral (Rolling) Constraint

 

and

Where:

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Kinematic Constraints

 

Rolling Motion Constraints

Lateral Motion Constraints

 

 

 

 

 

 

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Maneuverability

 

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Maneuverability

 

 

 

 

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Maneuverability

 

Bicycle Steering

Ackermann Steering

 

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Maneuverability

 

 

 

where:

 

 

(i.e. dimension of vector space spanned)

 

Sliding Constraint:

 

 

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Maneuverability

 

where:

(i.e. dimension of vector space spanned)

 

Sliding Constraint:

 

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Maneuverability

 

where:

(i.e. dimension of vector space spanned)

 

Sliding Constraint:

 

 

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Maneuverability

 

where:

(i.e. dimension of vector space spanned)

 

Sliding Constraint:

 

(no motion allowed – rank is 3)

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Maneuverability

 

 

 

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Maneuverability

 

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Differential Drive Kinematic Model

 

 

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Differential Drive Kinematic Model

 

 

 

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Time for Questions !

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CS-791