Safe Pontryagin Differentiable Programming

TL;DR

Safe Pontryagin Differentiable Programming (Safe PDP) provides a theoretical framework for safety-critical learning and control tasks, ensuring safety constraints are satisfied at all stages through barrier functions and efficient approximations.

Contribution

It introduces a novel Safe PDP methodology that guarantees safety throughout learning and control by integrating barrier functions and efficient unconstrained problem solutions.

Findings

Successfully applied to safe policy optimization

Effective in safe motion planning for complex systems

Demonstrated safety guarantees in learning MPCs from demonstrations

Abstract

We propose a Safe Pontryagin Differentiable Programming (Safe PDP) methodology, which establishes a theoretical and algorithmic framework to solve a broad class of safety-critical learning and control tasks -- problems that require the guarantee of safety constraint satisfaction at any stage of the learning and control progress. In the spirit of interior-point methods, Safe PDP handles different types of system constraints on states and inputs by incorporating them into the cost or loss through barrier functions. We prove three fundamentals of the proposed Safe PDP: first, both the solution and its gradient in the backward pass can be approximated by solving their more efficient unconstrained counterparts; second, the approximation for both the solution and its gradient can be controlled for arbitrary accuracy by a barrier parameter; and third, importantly, all intermediate results throughout the approximation and optimization strictly respect the constraints, thus guaranteeing safety throughout the entire learning and control process. We demonstrate the capabilities of Safe PDP in solving various safety-critical tasks, including safe policy optimization, safe motion planning, and learning MPCs from demonstrations, on different challenging systems such as 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing.