Safe Imitation Learning of Nonlinear Model Predictive Control for Flexible Robots

Method

Nonlinear MPC performance

nmpc_performance.mp4

The proposed method vs NMPC

nmpc_vs_method.mp4

Installation of acados:

Installation of acados according to the following instructions: https://docs.acados.org/python_interface/index.html

Imitation Library Fork (submodule):

Current (21 August 2023) version on imitation library does not yet support Gymnasium. So we are using our own fork of it with necessary modifications.

After cloning this repo:

• git submodule init
• git submodule update
• cd imitation
• pip install -e .

Hyperparameters of the IL, RL and IRL algorithms

Hyper-parameter	Value
COMMON: Learning Rate	0.0003
COMMON: Number of Expert Demos	100
COMMON: Number of Training Steps	2,000,000
PPO: Net. Arch.	pi:[256, 256] vf:[256, 256]
PPO: Batch Size	64
SAC: Net. Arch.	pi:[256, 256] qf:[256, 256]
SAC: Batch Size	256
BC: Net. Arch.	pi:[32, 32] qf:[32, 32]
BC: Batch Size	32
DAgger: Online Episodes	500
Density: Kernel type	Gaussian
Density: Kernel bandwidth	0.5
Density: Net. Arch.	pi:[256, 256] qf:[256, 256]
GAIL: Reward Net Arch.	[32, 32]
GAIL: Policy Net Arch.	pi:[256, 256] qf:[256, 256]
GAIL: Policy Replay Buffer Capacity	512
GAIL: Batch Size	128
AIRL: Reward Net Arch.	[32, 32]
AIRL: Policy Net Arch.	pi:[256, 256] qf:[256, 256]
AIRL: Batch Size	128
AIRL: Policy Replay Buffer Capacity	512

NMPC parameters

Parameter	Value
Hessian Approximation	Gauss-Newton
SQP type	real-time iterations
$\Delta t$, $N$, $n_\mathrm{seg}$	$5$ ms, 125, 3
$Q$ weights $w_{q_a}$, $\dot w_{q_a}$, $w_{q_p}$, $\dot{w}_{q_p}$	$0.01 ; 0.1 ; 0.01 ; 10$
$P_N$	diag($[1,1,1,0,0,0])\cdot 10^4$
$P$	diag($[1,1,1,0,0,0])\cdot 2\cdot10^3$
$R$	diag($[1,10,10]$)
$S$, $s$	diag($[1,1,1]\cdot 10^6$), $[1,1,1]^\top\cdot 10^4$
$\delta_\mathrm{ee}, \delta_\mathrm{elb}$ , $\delta_\mathrm{x}$	$0.01\mathrm{m}, ;0.005\mathrm{m}$, ; $0\cdot 1_{n_x}$
$\overline{\dot{q_a}}=-\underline{\dot{q_a}}$	$[2.5, 3.5, 3.5]^\top;s^{-1}$
$\overline{u}=-\underline{u}$	$[20,10,10]^\top$ Nm

Safety Filter parameters

Parameter	Value
$\Delta t_\mathrm{SF}$, $N_\mathrm{SF}$, $n_\mathrm{seg}$	$10$ ms, $25$, $1$
$\bar{R}$	diag($[1,1,1]$)
${R}_\mathrm{SF}$	diag($[1,1,1]$) $\cdot 10^{-5}$