Differential Dynamic Programming with Nonlinear Safety Constraints Under System Uncertainties

Gökhan Alcan*, Ville Kyrki

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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 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.
Original languageEnglish
Number of pages8
JournalIEEE Robotics and Automation Letters
Volume7
Issue number2
DOIs
Publication statusPublished - Apr 2022
MoE publication typeA1 Journal article-refereed

Keywords

  • Optimization and Optimal Control
  • Constrained Motion Planning
  • Planning Under Uncertainty
  • Robot Safety
  • Motion and Path Planning

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