Model_predictive_control

MPC using various optimisation algorithms

Instructions to run:

• Clone the repository:

  git clone https://github.com/susiejojo/Model_predictive_control.git

• cd into the directory and make a new /data directory. This can be done by:

  mkdir data

• Open in MATLAB and execute run.m.

• The simulation images are saved under /data.

• To generate videos, copy mkmovie.sh into the /data folder and execute the shell script by:

  ./mkmovie.sh.

Files and directories:

• run.m: main code to generate simulations, and run the optimisation routine.
• getPreds.m: used to return predictions based on waypoints for a prediction horizon. Uses L2 norm for cost, L2 regularisation of w.
• nonhn_pts.m: used to generate the x,y coordinates given a set of linear and angular velocities.
• plot_figs.m: used to plot the simulation frame by frame. Adjusts the heading and position of the agent as given by the optimiser.
• colnfn.m: returns collision constraints and lane constraints. Contains flags has_obstacle and has_lane_con to toggle constraints.
• mkmovie.sh: used to generate video from the image frames obtained from MATLAB.
• /data: stores the images frame by frame for the simulation. Also on running the video generator code, generates simulation.mp4.
• /results: stores the simulations obtained during testing.

Results:

• All the results below have been obtained with planning_horizon = 50 and control_horizon = 10.
• The green points denote the positions returned by the planner over the planning horizon.
• The blue trajectory is the actual path followed by the bot.
• The black dashed lines denote lane constraints.
• Obstacle has been assumed to be a circle of a given radius.
• Initial w and v: v = 1, w = uniform(-0.06,0.06)
• vmin = 0, vmax = 20, wmin = -0.1 wmax = 0.1. (Till Video7), wmin = -0.5, wmax = 0.5 for Videos 8,9.
• MaxFunctionEvaluations = 30000,MaxIterations = 10000 for Videos 8 and 9.
• Lane Constraints(where applicable in case of y=x): left => y = x+25, right => y = x-25

Scenario	Initial heading	Waypoints	End orientation constraint	Obstacle	Lane Constraint	Video
Move from (0,0) to (125,125)	pi/4	50 waypoints, equally spaced	None	None	None	Video1
Move from (0,0) to (80,80)	0	1 waypoint at goal	None	None	None	Video2
Move from (0,0) to (80,80)	pi/4	1 waypoint at goal	None	None	None	Video3
Move from (0,0) to (50,0)	0	1 waypoint at goal	None	None	None	Video4
Move from (0,0) to (50,0)	0	1 waypoint at goal	None	(30,0)	None	Video5
Move from (0,0) to (80,80)	pi/4	1 waypoint at goal	0	None	None	Video6
Move from (0,0) to (80,80)	pi/4	1 waypoint at goal	None	(30,30)	None	Video8
Move from (0,0) to (80,80)	pi/4	1 waypoint at goal	None	(30,30)	As in video	Video9
Move from (0,0) to (50,50)	pi/4	1 waypoint at goal	0	(30,30)	As in video	Video10

Observations and Points to Remember:

• Uniformly distributed w vs fixed positive and negative w.
• Norm of vector vs norm of matrix
• Adjusting values of vmax and plotting v w.r.t time to ensure a smooth graph
• Setting acceleration constraints to ensure smoothness of v.
• Removing collision constraint once the bot has passed the obstacle and is ahead of it.
• Fine-tuning weights for end orientation constraint
• Adjusting values of wmax for making achieving end orientation constraints feasible.
• Feasilibity of reaching goal vs values of vmax and vmin, time step and planning horizon
• Difference between multiple waypoints and a single waypoint
• fmincon requires manual tuning of MaxIterations and MaxFunctionEvaluations to be able to complete the optimization routine.
• Learnt about fmincon exit codes, and read up fmincon documentation for options parameters.