Differential Dynamic Programming with Nonlinear Safety Constraints Under System Uncertainties
This addresses safe operation for robots under uncertainties, representing an incremental improvement in constrained trajectory optimization.
The paper tackles the problem of ensuring robot safety under system uncertainties by proposing Safe-CDDP, a trajectory optimization method that transforms chance constraints into deterministic ones via constraint tightening, achieving constraint satisfaction with user-chosen probabilities and demonstrating feasibility on robots with up to 12 degrees of freedom in simulation and hardware.
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.