2PAC: Two-Point Attractors for Center Of Mass Trajectories in Multi-Contact Scenarios

Steve Tonneau, Pierre Fernbach, Andrea Del Prete, Julien Pettré, Nicolas Mansard

Research output: Contribution to journalArticlepeer-review


Synthesizing motions for legged characters in arbitrary environments is a long-standing problem that has recently received a lot of attention from the computer graphics community. We tackle this problem with a procedural approach that is generic, fully automatic, and independent from motion capture data. The main contribution of this article is a point-mass-model-based method to synthesize Center Of Mass trajectories. These trajectories are then used to generate the whole-body motion of the character.

The use of a point mass model results in physically inconsistent motions and joint limit violations when mapped back to a full- body motion. We mitigate these issues through the use of a novel formulation of the kinematic constraints that allows us to generate a quasi-static Center Of Mass trajectory in a way that is both user-friendly and computationally efficient. We also show that the quasi-static constraint can be relaxed to generate motions usable for computer animation at the cost of a moderate violation of the dynamic constraints.

Our method was integrated in our open-source contact planner and tested with different scenarios—some never addressed before—featuring legged characters performing non-gaited motions in cluttered environments. The computational efficiency of our trajectory generation algorithm (under one ms to compute one second of trajectory) enables us to synthesize motions in a few seconds, one order of magnitude faster than state-of-the-art methods. Although our method is empirically able to synthesize collision-free motions, the formal handling of environmental constraints is not part of the proposed method and left for future work.
Original languageEnglish
Article number176
Pages (from-to)176:1-176:14
Number of pages15
JournalACM Transactions on Graphics
Issue number5
Publication statusPublished - 26 Nov 2018


  • Center Of Mass
  • Character animation
  • motion planning
  • multi-contact locomotion
  • physical simulation

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