Smooth Model Predictive Path Integral Control Without Smoothing

Abstract

We present a sampling-based control approach that can generate smooth actions for general nonlinear systems without external smoothing algorithms. Model Predictive Path Integral (MPPI) control has been utilized in numerous robotic applications due to its appealing characteristics to solve nonconvex optimization problems. However, the stochastic nature of sampling-based methods can cause significant chattering in the resulting commands. Chattering becomes more prominent in cases where the environment changes rapidly, possibly even causing the MPPI to diverge. To address this issue, we propose a method that seamlessly combines MPPI with an input-lifting strategy. In addition, we introduce a new action cost to smooth control sequence during trajectory rollouts while preserving the information theoretic interpretation of MPPI, which was derived from non-affine dynamics. We validate our method in two nonlinear control tasks with neural network dynamics: a pendulum swing-up task and a challenging autonomous driving task. The experimental results demonstrate that our method outperforms the MPPI baselines with additionally applied smoothing algorithms.

Shopping with AI: Consumers' perceived autonomy in the age of AI

“…Gaussian noise to each dynamic state observation in x. MPPI is used in the active exploration experiments (Q1), and SMPPI is used in the deployment experiments (Q2-Q3). Table I lists the parameters of two controllers, while the remaining parameters not specified in this paper are taken from the SMPPI implementation [43]. We use a four-layer MLP with the hidden layer sizes {40, 80, 120, 40} throughout all experiments.…”

“…In this phase, we use a variant of the MPPI algorithm called Smooth MPPI (SMPPI) [43]. SMPPI shares the same information-theoretic roots as MPPI, and it also benefits from the structure of parallel trajectory evaluation.…”

“…where ω ∈ R m×m is the weighting parameter. Such action cost was not eligible in the MPPI baseline with non-affine dynamics because it violates the information theoretic derivation [43]. As a result of these smoothing effects, SMPPI is not suitable for rapid exploration in underactuated continuous control systems but is beneficial for deployment.…”

Real-Time Drift-Driving Control for an Autonomous Vehicle: Learning from Nonlinear Model Predictive Control via a Deep Neural Network

“…However, significant chattering of the optimal sequence may occur due to the stochastic process of this samplingbased algorithm. To resolve this problem, we utilize the Smooth MPPI (SMPPI) approach proposed in our prior work [27], which effectively attenuates chattering while adapting to a rapidly changing environment. Similar to prior work [22], we add the following three components to c(x):…”

A fault-tolerant and robust controller using model predictive path integral control for free-flying space robots

“…Moreover, MPPI’s performance depends considerably on the number of trajectories sampled using the on-board model, and the embedding computation can benefit from recent advances in Graphics Processing Units (GPUs) to achieve better real-time performance. It means one can adjust MPPI performance in real-world applications by selecting suitable processors ( Arruda et al., 2017 ; Kim et al., 2022 ). MPPI has been used to control aerial and terrestrial robots ( Williams et al., 2016 ; Pravitra et al., 2020 ).…”