Guy and Seth on Simulink
March 6th, 2009
Models Inspired by Real Life
models are the predecessor to a real-life device; however, sometimes a device
inspires the model. In the 1980s, there was a group known as the Leg Lab at CMU
who researched running robots. In 1986 the Leg Lab moved to MIT. Some of
their robots are now on display at the MIT
Museum, and they
still inspire wonder in visitors today. One of those robots is a 3-D One-Legged Hopper which inspired my colleague, Guy Rouleau.
I saw this robot at the MIT Museum last winter and after discussing with few
colleagues at The MathWorks we decided that it would be cool to have a Simulink
model of this robot.
Read on to
learn about how Guy constructed and controlled this one-legged hopper (download from the file exchange).
and Control of a One-Legged Hopping Robot
is the description of a one-legged hopping robot Simulink model I completed
recently. I will explain how I prepared and implemented this simulation.
modeling any system in Simulink, it is always good to have a plan. To begin I always
like to draw a simple representation of the system I want to model. In this
picture we see two bodies (let’s call them body and leg)
connected together at the hip. The robot has two actuated degrees of freedom
(DoF) in his configuration space, the angle between the body and the leg, and
the length of the leg. These 2 DoF will be used to control the 3 DoF motion of
the body in space (height, distance and angle).
that the robot is described, it is time to think about how to control it. The robot
control can be divided into three independent controllers:
- Attitude Control - The length of the leg is controlled
by a pneumatic actuator. This actuator behaves like a spring. It gives a smooth
landing and injects force to keep the robot bouncing.
- Velocity Control – As when a person walks, the leg is
brought in front of the body while it is in the air. While the leg touches the
ground, then the body is brought in front.
- Orientation Control - During the
stance, the leg is in contact with the ground. A torque is applied at the hip
to control the angle of the body.
following picture shows the three controllers graphically:
I have a good idea of what to implement, it is time to have fun and play with
Simulink. For this model, SimMechanics is the most appropriate Blockset to
model the robot.
I begin a SimMechanics model for a moving robot, I like fixing the position of
the body in space. By doing so, I can verify if the configuration of the
actuators behaves as expected. This SimMechanics model looks like this:
this model I can test different inputs and see the resulting motion at the tip
of the leg. Once I am satisfied with this motion, I can think about the
interaction with the ground.
new goal is now to see the robot falling from a certain initial eight, bouncing
a few times and fall. To model the ground, I use the Bouncing Ball demo
provided with SimMechanics. After grouping components within subsystems, the
model now looks like the following picture.
the contact forces and robot motion are validated, it is time to implement the
when I implement a controller I like to divide the model in the following
This subsystem extracts and processes
the information from the SimMechanics model to generate signals that could be
provided by real sensors. For the hopping robot, I will measure the following:
- Angle between leg and body
- Angle of the body relative to the ground
- An on/off contact sensor.
Based on the sensors, the
information necessary for the controllers is computed. The contact switch is
used to compute the duration of the flight and stance period. These durations,
along with the hip and body angles can be used to estimate the robot velocity
With all the necessary information
available, it is time to generate the actuator signals for the 3 control modes.
– The same amount of force is injected by the pneumatic actuator at each
jump. This generates jumps of constant eight and duration. The amount of
force injected can be adjusted to obtain the desired jump eight, but for now,
it will be kept constant.
- Velocity – This is the most complex controller in this robot.
First, we look at the displacement during the previous jump. While in
flight, the tip of the leg is positioned in front of the robot body to
prepare a motion similar to the previous jump. Also during flight, the leg
tip position is modified depending if the robot must accelerate or
decelerate. Landing with the leg farther in front of the body will
accelerate the robot, while a leg tip closer to the body will decelerate
it. A simple trajectory generation is also implemented to move the leg
smoothly during the flight.
- Orientation – In this phase, a hip torque is computed to keep
the angle of the body with the ground close to zero. Combined with the
Velocity controller, the Orientation controller pushes the robot in the
implementing the 3 controllers, it is time to visualize what the resulting
motion looks like.
description above contains the main steps I followed to create the hopping
robot simulation. For more details, I suggest visiting the MATLAB Central File
Exchange to download the Simulink model of this one-legged hopping robot.
looking at the model, you will see that I omitted many details to make a short
story. But the main process I use to create most of Simulink models is
ever built a robot? What do you think about this model? Please leave a comment here.
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