Differentiable Predictive Control for Robotics: A Data-Driven Predictive Safety Filter Approach

TL;DR

This work tackles the trade-off between safety and computational burden in robotics control by introducing differentiable predictive control (DPC) enhanced with a dynamics-decomposition based on Vector Relative Degree (VRD), a data-driven safe set, and an event-driven Predictive Safety Filter (PSF). The approach enables offline training of a neural policy that approximates MPC while maintaining safety via a data-derived safe region and a lightweight online safety correction. On a quadcopter, DPC achieves MPC-like performance with up to three orders of magnitude faster online computation and maintains safety even in unseen scenarios when augmented with PSF. The results demonstrate practical viability for real-time, learning-based control in resource-constrained robots, while identifying avenues for guaranteed-safety extensions.

Abstract

Model Predictive Control (MPC) is effective at generating safe control strategies in constrained scenarios, at the cost of computational complexity. This is especially the case in robots that require high sampling rates and have limited computing resources. Differentiable Predictive Control (DPC) trains offline a neural network approximation of the parametric MPC problem leading to computationally efficient online control laws at the cost of losing safety guarantees. DPC requires a differentiable model, and performs poorly when poorly conditioned. In this paper we propose a system decomposition technique based on relative degree to overcome this. We also develop a novel safe set generation technique based on the DPC training dataset and a novel event-triggered predictive safety filter which promotes convergence towards the safe set. Our empirical results on a quadcopter demonstrate that the DPC control laws have comparable performance to the state-of-the-art MPC whilst having up to three orders of magnitude reduction in computation time and satisfy safety requirements in a scenario that DPC was not trained on.

Figures (6)

• Figure 1: DPC + PSF formulation overview
• Figure 2: Robust $\delta$ Applied to $\mathcal{S}_{\mathbb{V}1}$
• Figure 3: Illustration of a single face of a safe set convex hull being used as a constraint in the PSF at every timestep
• Figure 4: Trajectory Tracking Task Mujoco Render
• Figure 5: Trajectory Tracking Task

Theorems & Definitions (3)

• Definition 1: Vector Relative Degree
• Definition 2: Well-Defined Vector Relative Degree
• Definition 3: $\pmb{\Delta}$