Differential Dynamic Programming with Nonlinear Safety Constraints Under System Uncertainties

TL;DR

This paper introduces Safe-CDDP, a novel trajectory optimization method that ensures safety under uncertainties by transforming chance constraints into deterministic ones within a constrained DDP framework, validated on robotic systems.

Contribution

The paper presents Safe-CDDP, integrating chance constraints with constrained DDP for safe robot trajectory planning under nonlinear safety constraints and uncertainties.

Findings

Effective in simulation with robots up to 12 DOF

Demonstrated real-time feasibility on hardware

Reduces over-conservatism with feedback control gains

Abstract

Safe operation of systems such as robots requires them to plan and execute trajectories subject to safety constraints. When those systems are subject to uncertainties in their dynamics, it is challenging to ensure that the constraints are not violated. In this paper, we propose Safe-CDDP, a safe trajectory optimization and control approach for systems under additive uncertainties and non-linear safety constraints based on constrained differential dynamic programming (DDP). The safety of the robot during its motion is formulated as chance constraints with user-chosen probabilities of constraint satisfaction. The chance constraints are transformed into deterministic ones in DDP formulation by constraint tightening. To avoid over-conservatism during constraint tightening, linear control gains of the feedback policy derived from the constrained DDP are used in the approximation of closed-loop uncertainty propagation in prediction. The proposed algorithm is empirically evaluated on three different robot dynamics with up to 12 degrees of freedom in simulation. The computational feasibility and applicability of the approach are demonstrated with a physical hardware implementation.