icra21.md

Reproduce Figures from ICRA 2021 Paper

Figure 3

Reach-SDP (Final Step Error: 206):

python -m nfl_veripy.example \
	--partitioner None \
	--propagator SDP \
	--system double_integrator \
	--state_feedback \
	--t_max 5 \
	--save_plot --skip_show_plot

Note: If SDP isn't working, consider using a different solver and/or making it verbose (look for prob.solve(**solver_args) in ClosedLoopSDPPropagator). If you have MOSEK installed, you could add the arg --cvxpy_solver MOSEK to use it, as the example script uses cvxpy's default solver as is.

Reach-SDP-Partition (Final Step Error: 19.35):

python -m nfl_veripy.example \
	--partitioner Uniform \
	--propagator SDP \
	--system double_integrator \
	--state_feedback \
	--t_max 5 \
	--save_plot --skip_show_plot

Reach-LP (Final Step Error: 848):

python -m nfl_veripy.example \
	--partitioner None \
	--propagator CROWN \
	--system double_integrator \
	--state_feedback \
	--t_max 5 \
	--save_plot --skip_show_plot

Reach-LP-Partition (Final Step Error: 19.87):

python -m nfl_veripy.example \
	--partitioner Uniform \
	--propagator CROWN \
	--system double_integrator \
	--state_feedback \
	--t_max 5 \
	--save_plot --skip_show_plot

Add the --estimate_runtime flag to any of those to see how long it takes to run each algorithm (avg. over 5 trials) on your machine!

Reach-SDP	Reach-SDP-Partition	Reach-LP	Reach-LP-Partition

Figure 4

For Fig. 4b, use a polytope description of the reachable sets with different numbers of facets (just change --num_polytope_facets):

python -m nfl_veripy.example \
	--partitioner None \
	--propagator CROWN \
	--system double_integrator \
	--state_feedback \
	--t_max 4 \
	--save_plot --skip_show_plot \
	--boundaries polytope \
	--num_polytope_facets 8 \
	--init_state_range "[[-2., -1.5], [0.4, 0.8]]"

Note: currently this doesn't use the right NN model that was trained to drive the system to the origin from this initial state set, but the idea is the same.

4-Polytope (Rectangle)	8-Polytope	35-Polytope

Figure 5

Fig 5a (no noise ==> --state_feedback):

python -m nfl_veripy.example \
	--partitioner None \
	--propagator CROWN \
	--system quadrotor \
	--state_feedback \
	--t_max 1.2 \
	--save_plot --skip_show_plot \
	--boundaries lp \
	--plot_aspect equal

Fig 5b (process & sensor noise ==> --output_feedback):

python -m nfl_veripy.example \
	--partitioner None \
	--propagator CROWN \
	--system quadrotor \
	--output_feedback \
	--t_max 1.2 \
	--save_plot --skip_show_plot \
	--boundaries lp \
	--plot_aspect equal

No Noise	Noise