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Unit 2: MobilityMethods of Locomotion
Computer Science 4766/6778
Department of Computer ScienceMemorial University of Newfoundland
January 27, 2009
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 1 / 14
1 Introduction
2 Legged Robots
3 Wheeled Robots
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 2 / 14
Methods of Locomotion
In nature, we see many varieties of locomotion:
walking, jumping, running, sliding, skating, swimming, flying, rolling,...
The wheel is not found in nature, but is highly efficient on flat ground
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 3 / 14
Methods of Locomotion
In nature, we see many varieties of locomotion:walking, jumping, running, sliding, skating, swimming, flying, rolling,...
The wheel is not found in nature, but is highly efficient on flat ground
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 3 / 14
Methods of Locomotion
In nature, we see many varieties of locomotion:walking, jumping, running, sliding, skating, swimming, flying, rolling,...
The wheel is not found in nature, but is highly efficient on flat ground
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 3 / 14
Methods of Locomotion
In nature, we see many varieties of locomotion:walking, jumping, running, sliding, skating, swimming, flying, rolling,...
The wheel is not found in nature, but is highly efficient on flat ground
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 3 / 14
Methods of Locomotion
In nature, we see many varieties of locomotion:walking, jumping, running, sliding, skating, swimming, flying, rolling,...
The wheel is not found in nature, but is highly efficient on flat ground
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 3 / 14
Legged Robots
Advantages:
Ability to travel over rough terrainLegs can double as object manipulators
Disadvantages:
Greater power needs, mechanical complexity, and control complexity
Degrees of freedom:
≥ 2 : one to lift, one to move leg forwardHigher numbers of degrees of freedom (e.g. 7 in human leg) affordgreater manoeuvrability and variety of gaits; But lead to additionalmass, energy, and complexity
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 4 / 14
Legged Robots
Advantages:
Ability to travel over rough terrain
Legs can double as object manipulators
Disadvantages:
Greater power needs, mechanical complexity, and control complexity
Degrees of freedom:
≥ 2 : one to lift, one to move leg forwardHigher numbers of degrees of freedom (e.g. 7 in human leg) affordgreater manoeuvrability and variety of gaits; But lead to additionalmass, energy, and complexity
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 4 / 14
Legged Robots
Advantages:
Ability to travel over rough terrainLegs can double as object manipulators
Disadvantages:
Greater power needs, mechanical complexity, and control complexity
Degrees of freedom:
≥ 2 : one to lift, one to move leg forwardHigher numbers of degrees of freedom (e.g. 7 in human leg) affordgreater manoeuvrability and variety of gaits; But lead to additionalmass, energy, and complexity
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 4 / 14
Legged Robots
Advantages:
Ability to travel over rough terrainLegs can double as object manipulators
Disadvantages:
Greater power needs, mechanical complexity, and control complexity
Degrees of freedom:
≥ 2 : one to lift, one to move leg forwardHigher numbers of degrees of freedom (e.g. 7 in human leg) affordgreater manoeuvrability and variety of gaits; But lead to additionalmass, energy, and complexity
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 4 / 14
Legged Robots
Advantages:
Ability to travel over rough terrainLegs can double as object manipulators
Disadvantages:
Greater power needs, mechanical complexity, and control complexity
Degrees of freedom:
≥ 2 : one to lift, one to move leg forwardHigher numbers of degrees of freedom (e.g. 7 in human leg) affordgreater manoeuvrability and variety of gaits; But lead to additionalmass, energy, and complexity
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 4 / 14
Legged Robots
Advantages:
Ability to travel over rough terrainLegs can double as object manipulators
Disadvantages:
Greater power needs, mechanical complexity, and control complexity
Degrees of freedom:
≥ 2 : one to lift, one to move leg forwardHigher numbers of degrees of freedom (e.g. 7 in human leg) affordgreater manoeuvrability and variety of gaits; But lead to additionalmass, energy, and complexity
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 4 / 14
Legged Robots
Advantages:
Ability to travel over rough terrainLegs can double as object manipulators
Disadvantages:
Greater power needs, mechanical complexity, and control complexity
Degrees of freedom:
≥ 2 : one to lift, one to move leg forward
Higher numbers of degrees of freedom (e.g. 7 in human leg) affordgreater manoeuvrability and variety of gaits; But lead to additionalmass, energy, and complexity
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 4 / 14
Legged Robots
Advantages:
Ability to travel over rough terrainLegs can double as object manipulators
Disadvantages:
Greater power needs, mechanical complexity, and control complexity
Degrees of freedom:
≥ 2 : one to lift, one to move leg forwardHigher numbers of degrees of freedom (e.g. 7 in human leg) affordgreater manoeuvrability and variety of gaits; But lead to additionalmass, energy, and complexity
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 4 / 14
Stability:
A robot with three or more legs exhibits static stability if its centre ofmass is within the triangle formed by any three legs
A 6-legged robot can exhibit static walking by using the “tripod gait”(video)
Two-legged robots can exhibit only dynamic stability (i.e. forces mustbe applied to maintain balance)
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 5 / 14
Stability:A robot with three or more legs exhibits static stability if its centre ofmass is within the triangle formed by any three legs
A 6-legged robot can exhibit static walking by using the “tripod gait”(video)
Two-legged robots can exhibit only dynamic stability (i.e. forces mustbe applied to maintain balance)
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 5 / 14
Stability:A robot with three or more legs exhibits static stability if its centre ofmass is within the triangle formed by any three legs
A 6-legged robot can exhibit static walking by using the “tripod gait”(video)
Two-legged robots can exhibit only dynamic stability (i.e. forces mustbe applied to maintain balance)
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 5 / 14
Stability:A robot with three or more legs exhibits static stability if its centre ofmass is within the triangle formed by any three legs
A 6-legged robot can exhibit static walking by using the “tripod gait”(video)
Two-legged robots can exhibit only dynamic stability (i.e. forces mustbe applied to maintain balance)
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 5 / 14
Wheeled Robots
Advantages:
Simpler, cheaper, faster, more efficient than legsStability constraint same as for legged robots (centre of mass withinthe triangle formed by 3 wheels) although the wheels usually stay onthe ground
Disadvantages:
Suspension system may be requiredRestricted to flat terrain (overcome by hybrids such as the Mars rovers)
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 6 / 14
Wheeled Robots
Advantages:
Simpler, cheaper, faster, more efficient than legs
Stability constraint same as for legged robots (centre of mass withinthe triangle formed by 3 wheels) although the wheels usually stay onthe ground
Disadvantages:
Suspension system may be requiredRestricted to flat terrain (overcome by hybrids such as the Mars rovers)
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 6 / 14
Wheeled Robots
Advantages:
Simpler, cheaper, faster, more efficient than legsStability constraint same as for legged robots (centre of mass withinthe triangle formed by 3 wheels) although the wheels usually stay onthe ground
Disadvantages:
Suspension system may be requiredRestricted to flat terrain (overcome by hybrids such as the Mars rovers)
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 6 / 14
Wheeled Robots
Advantages:
Simpler, cheaper, faster, more efficient than legsStability constraint same as for legged robots (centre of mass withinthe triangle formed by 3 wheels) although the wheels usually stay onthe ground
Disadvantages:
Suspension system may be requiredRestricted to flat terrain (overcome by hybrids such as the Mars rovers)
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 6 / 14
Wheeled Robots
Advantages:
Simpler, cheaper, faster, more efficient than legsStability constraint same as for legged robots (centre of mass withinthe triangle formed by 3 wheels) although the wheels usually stay onthe ground
Disadvantages:
Suspension system may be required
Restricted to flat terrain (overcome by hybrids such as the Mars rovers)
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 6 / 14
Wheeled Robots
Advantages:
Simpler, cheaper, faster, more efficient than legsStability constraint same as for legged robots (centre of mass withinthe triangle formed by 3 wheels) although the wheels usually stay onthe ground
Disadvantages:
Suspension system may be requiredRestricted to flat terrain (overcome by hybrids such as the Mars rovers)
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 6 / 14
Wheel designs: Four main types
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 7 / 14
Castor wheels differ from standard wheels in that a Castor wheelrotates about an axis which is offset from the centre of the wheel
If steered, a Castor wheel exerts a force on the robot; Not so forstandard wheelsThis gives Castor wheels an advantage of sorts—if a forceperpendicular to the wheel is applied, the Castor wheel can move toaccommodate this force; a standard wheel cannot
Swedish and spherical wheels can also move to accommodate a forceapplied at any angle
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 8 / 14
Castor wheels differ from standard wheels in that a Castor wheelrotates about an axis which is offset from the centre of the wheel
If steered, a Castor wheel exerts a force on the robot; Not so forstandard wheels
This gives Castor wheels an advantage of sorts—if a forceperpendicular to the wheel is applied, the Castor wheel can move toaccommodate this force; a standard wheel cannot
Swedish and spherical wheels can also move to accommodate a forceapplied at any angle
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 8 / 14
Castor wheels differ from standard wheels in that a Castor wheelrotates about an axis which is offset from the centre of the wheel
If steered, a Castor wheel exerts a force on the robot; Not so forstandard wheelsThis gives Castor wheels an advantage of sorts—if a forceperpendicular to the wheel is applied, the Castor wheel can move toaccommodate this force; a standard wheel cannot
Swedish and spherical wheels can also move to accommodate a forceapplied at any angle
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 8 / 14
Castor wheels differ from standard wheels in that a Castor wheelrotates about an axis which is offset from the centre of the wheel
If steered, a Castor wheel exerts a force on the robot; Not so forstandard wheelsThis gives Castor wheels an advantage of sorts—if a forceperpendicular to the wheel is applied, the Castor wheel can move toaccommodate this force; a standard wheel cannot
Swedish and spherical wheels can also move to accommodate a forceapplied at any angle
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 8 / 14
Swedish Wheels
The small rollers are passive, but provide the ability to role in anadditional direction
The rollers above are at 45◦ to the wheel axis, those below are at 90◦
www.acroname.com/robotics/info/PPRK/overview.html
Swedish Wheels
The small rollers are passive, but provide the ability to role in anadditional direction
The rollers above are at 45◦ to the wheel axis, those below are at 90◦
www.acroname.com/robotics/info/PPRK/overview.html
Swedish Wheels
The small rollers are passive, but provide the ability to role in anadditional direction
The rollers above are at 45◦ to the wheel axis, those below are at 90◦
www.acroname.com/robotics/info/PPRK/overview.html
Swedish Wheels
The small rollers are passive, but provide the ability to role in anadditional direction
The rollers above are at 45◦ to the wheel axis, those below are at 90◦
www.acroname.com/robotics/info/PPRK/overview.html
Swedish Wheels
The small rollers are passive, but provide the ability to role in anadditional direction
The rollers above are at 45◦ to the wheel axis, those below are at 90◦
www.acroname.com/robotics/info/PPRK/overview.html
Swedish Wheels
The small rollers are passive, but provide the ability to role in anadditional direction
The rollers above are at 45◦ to the wheel axis, those below are at 90◦
www.acroname.com/robotics/info/PPRK/overview.html
Swedish Wheels
The small rollers are passive, but provide the ability to role in anadditional direction
The rollers above are at 45◦ to the wheel axis, those below are at 90◦
www.acroname.com/robotics/info/PPRK/overview.html
Swedish Wheels
The small rollers are passive, but provide the ability to role in anadditional direction
The rollers above are at 45◦ to the wheel axis, those below are at 90◦
www.acroname.com/robotics/info/PPRK/overview.html
Wheel Configurations: Notation
A variety of different wheel configurations follow...
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 10 / 14
Wheel Configurations: Notation
A variety of different wheel configurations follow...
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 10 / 14
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 11 / 14
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 12 / 14
Wheel Configurations
Various criteria impact the utility of a particular configuration:
Stability:
A 2-wheel robot can exhibit static stability if the centre of mass isbelow the common axleOtherwise, 3 wheels required
Manoeuvrability (addressed in “kinematics”)Controllability
e.g. Driving a robot with Swedish wheels in a straight line may bedifficult; The passive rollers introduce extra slippage; This slippage ishard to compensate for because it is hard to measure
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 13 / 14
Wheel Configurations
Various criteria impact the utility of a particular configuration:Stability:
A 2-wheel robot can exhibit static stability if the centre of mass isbelow the common axleOtherwise, 3 wheels required
Manoeuvrability (addressed in “kinematics”)Controllability
e.g. Driving a robot with Swedish wheels in a straight line may bedifficult; The passive rollers introduce extra slippage; This slippage ishard to compensate for because it is hard to measure
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 13 / 14
Wheel Configurations
Various criteria impact the utility of a particular configuration:Stability:
A 2-wheel robot can exhibit static stability if the centre of mass isbelow the common axle
Otherwise, 3 wheels required
Manoeuvrability (addressed in “kinematics”)Controllability
e.g. Driving a robot with Swedish wheels in a straight line may bedifficult; The passive rollers introduce extra slippage; This slippage ishard to compensate for because it is hard to measure
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 13 / 14
Wheel Configurations
Various criteria impact the utility of a particular configuration:Stability:
A 2-wheel robot can exhibit static stability if the centre of mass isbelow the common axleOtherwise, 3 wheels required
Manoeuvrability (addressed in “kinematics”)Controllability
e.g. Driving a robot with Swedish wheels in a straight line may bedifficult; The passive rollers introduce extra slippage; This slippage ishard to compensate for because it is hard to measure
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 13 / 14
Wheel Configurations
Various criteria impact the utility of a particular configuration:Stability:
A 2-wheel robot can exhibit static stability if the centre of mass isbelow the common axleOtherwise, 3 wheels required
Manoeuvrability (addressed in “kinematics”)
Controllability
e.g. Driving a robot with Swedish wheels in a straight line may bedifficult; The passive rollers introduce extra slippage; This slippage ishard to compensate for because it is hard to measure
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 13 / 14
Wheel Configurations
Various criteria impact the utility of a particular configuration:Stability:
A 2-wheel robot can exhibit static stability if the centre of mass isbelow the common axleOtherwise, 3 wheels required
Manoeuvrability (addressed in “kinematics”)Controllability
e.g. Driving a robot with Swedish wheels in a straight line may bedifficult; The passive rollers introduce extra slippage; This slippage ishard to compensate for because it is hard to measure
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 13 / 14
Wheel Configurations
Various criteria impact the utility of a particular configuration:Stability:
A 2-wheel robot can exhibit static stability if the centre of mass isbelow the common axleOtherwise, 3 wheels required
Manoeuvrability (addressed in “kinematics”)Controllability
e.g. Driving a robot with Swedish wheels in a straight line may bedifficult; The passive rollers introduce extra slippage; This slippage ishard to compensate for because it is hard to measure
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 13 / 14
References
COMP 4766/6778 (MUN) Methods of Locomotion January 27, 2009 14 / 14
![Locomotion [2015]](https://img.pdfslide.us/doc/110x75/55d39c9ebb61ebfd268b46a2/locomotion-2015.jpg)
