Differential Dynamic Programming With Nonlinear Safety Constraints Under System Uncertainties

• Published in: IEEE robotics and automation letters Vol. 7; no. 2; pp. 1760 - 1767
• Main Authors: Alcan, Gokhan, Kyrki, Ville
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.04.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; constrained motion planning; Constraints; Dynamic programming; Electron tubes; Linear control; motion and path planning; Optimization and optimal control; planning under uncertainty; Robot dynamics; robot safety; Robots; Safety; Stochastic processes; Task analysis; Tightening; Trajectory control; Trajectory optimization; Trajectory planning; Uncertainty
• ISSN: 2377-3766; 2377-3766
• DOI: 10.1109/LRA.2022.3141192

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 letter, we propose Safe-CDDP, a safe trajectory optimization and control approach for systems under additive uncertainties and nonlinear 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.