Simultaneous Contact, Gait, and Motion Planning for Robust Multilegged Locomotion via Mixed-Integer Convex Optimization

Bernardo Aceituno-Cabezas, Carlos Mastalli, Hongkai Dai, Michele Focchi, Andreea Radulescu, Darwin G. Caldwell, Jose Cappelletto, Juan C. Grieco, Gerardo Fernández-López, Claudio Semini

Research output: Contribution to journalArticlepeer-review


Traditional motion planning approaches for multi-legged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or nonconvex optimization within tractable computation time. In this letter, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions, and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a prespecified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot’s torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where nonconvexity and flat terrain assumptions might lead to suboptimal or unstable plans. Our method increases the motion robustness while keeping a low computation time.
Original languageEnglish
Pages (from-to)2531-2538
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number3
Early online date4 Dec 2017
Publication statusPublished - 31 Jul 2018


  • convex programming
  • integer programming
  • legged locomotion
  • motion control
  • multi-robot systems
  • optimisation
  • path planning
  • flat terrain condition
  • nonconvex optimization
  • mixed-integer convex formulation
  • gait transitions
  • friction cone stability margin
  • mixed-integer convex constraints
  • motion robustness
  • simultaneous contact
  • robust multilegged locomotion
  • mixed-integer convex optimization
  • contact search
  • trajectory generation
  • contacts
  • whole-body behaviors
  • fixed gait sequence
  • gait sequence
  • flat terrain
  • motion planning
  • robot torque
  • Legged locomotion
  • Dynamics
  • Planning
  • Optimization
  • Trajectory
  • Friction
  • Legged robots
  • motion and path planning
  • optimization and optimal control

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