In this assignment we will pose local planning as a optimization problem with constraints and use predictive control technique called as Model Predictive Control(MPC) to execute the plan. You need to have some understanding of optimization [1]. Please use the resource attached for discrete MPC(available on Moodle, MPC subsection).
Question:
Implement a discrete MPC planner for omni-wheel robot. You must implement the MPC algorithm for a two cases (i) With Obstacles (ii) Without Obstacles. You can use solvers like cvxopt in python or any other equivalent in Matlab.
• Your planner for a robot needs to satisfy various constraints on speed, acceleration, obstacle avoidance to make it feasible. Additionally your plan needs to optimize some aspect in your environment like speed, time or safety. Your plan should be n steps into the future.
You should frame Quadratic Programming QP for your planner to minimize goal reaching cost given by:
(xn − xg)2 + (yn − yg)2
robot model is given by
xt+dt = xt + vxt ∗ dt yt+dt = yt + vyt ∗ dt
velocity constraints are given by
0 ≤ vxi ≤ vmax
∀i ∈ [1,n]
0 ≤ vyi ≤ vmax
∀i ∈ [1,n]
• For (i)(with obstacles) : Extend the planner by adding circular obstacles. You can use euclidean distance constraint for obstacle avoidance. This adds Quadrtic constraint to Your problem. For example an static obstacle of radius r1 which is located at (xo,yo) then your constraint is given by.
