Contact-Implicit Trajectory Optimization using an Analytically Solvable Contact Model for Locomotion on Variable Ground

Iordanis Chatzinikolaidis, Yangwei You, Zhibin Li

Research output: Contribution to journalArticlepeer-review


This work presents a contact-implicit trajectory optimization framework utilizing an analytically solvable contact model to facilitate interactions with hard, soft, and slippery environments. Specifically, we propose a novel contact modeling that can be computed in closed-form, satisfies friction cone constraints and can be embedded into direct trajectory optimization frameworks without complementarity constraints. The closed-form solution decouples the computation of the contact forces from other actuation forces; this property is used to formulate a minimal direct optimization problem expressed with configuration variables only. Our simulation study demonstrates the characteristics and advantages over the rigid contact model and a trajectory optimization approach based on complementarity constraints. The proposed model enables physics-based optimization in a wide range of interactions with hard, slippery, and soft grounds in a unified manner, expressed by two parameters only. By computing trotting and jumping motions for a quadruped robot, the proposed optimization demonstrates the versatility of multi-contact motion planning on various surfaces with different physical properties.
Original languageEnglish
Pages (from-to)6357 - 6364
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number4
Early online date21 Jul 2020
Publication statusPublished - 1 Oct 2020


  • Optimization and Optimal Control
  • Multi-Contact Whole-Body Motion Planning and Control
  • Contact Modeling
  • Legged Robots

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