Bipedal Robotic Walker

The bipedal walker simulation code contains various functions that simulate the dynamics of a simple 3-link bipedal walker. The walker is modelled as a rigid body with three segments: a torso and two legs. The simulation is performed using the Euler-Lagrange equations of motion, and the gait is generated using a hybrid zero dynamics-based + impedance controller.
The simulation also includes a ground contact model and a collision handling method.
Run the code!

The main features are:

• The main script, solve_eqns.m, is used to simulate the dynamics of the bipedal walker. It takes as input the initial conditions of the system and the simulation parameters such as the duration of the simulation, the time step, and the number of steps to be taken. It returns the solution of the dynamics in the form of the state and control trajectories.

• The control function, control() implements the hybrid zero dynamics-based + impedance controller, which generates the desired torques for the two actuators (at the hip and inter-leg angles).
  NOTE that in this case, the impedance controller happens to coincide with a PD controller (altered definition of error term).

• The set_parameters() function is used to define the physical parameters of the robot, such as the masses and lengths of the links, and the acceleration due to gravity.

The remaining code is used to plot various metrics, such as the angles and velocities of the joints over time, the speed of the hip joint, the distance travelled by the bipedal walker in each step, the step frequency, and the torque applied to the actuators over time.
It also calculates the cost of transport, which is a measure of the energy efficiency of the gait.

For example, below we see how the average speed of the hip evolves:

For the full example plots, see the images in images folder.

Overall, the code provides a basic implementation of a 3-link bipedal walker and a simple hybrid zero dynamics + impedance controller.
The simulation results & metrics can be used to evaluate the performance of the controller and the efficiency of the gait.

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The parameters of the model are defined in the following image:

Note that the hyper-parameters of the control system are contained entirely within the control() script, not shown here.
Other notable scripts include:

• The kin_swf function calculates the kinematics of the swing foot during the stance phase of the gait. It takes as input the current state of the system and returns the position and velocity of the swing foot.

• The eqns function defines the metrics of interest. They are calculated during each time interval $\Delta t$ of te simulation. These contribute towards the energy calculations, average speed of the center of mass, etc...

Running the code

To run the simulation, download the repo and run the run_me.m script.
All folders must be in the same directory.
The animation will automatically start, and last $\sim 20$ seconds, then all of associated the metrics & plots will appear (8 plots, metrics in command window).

The command window should look like this: