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This research advances humanoid locomotion by introducing a contact-implicit optimization framework that enables dynamic movement across arbitrary, uneven terrains without predefined footstep sequences. By modeling ground geometry as smooth surfaces and incorporating novel contact constraints, the method extends planning capabilities from flat floors to complex topologies like steps and ramps. The approach validates feasibility through nonlinear programming on both simulation environments and the physical ErgoCub robot, marking a significant step toward robust real-world deployment.
Contact-Implicit Whole-Body Trajectory Optimization for Dynamic Humanoid Locomotion on Parameterizable Uneven Terrain
arXiv:2611.05585v1 Announce Type: new Abstract: This letter presents a trajectory planner for humanoid robots to perform dynamic motions on complex, parameterizable terrains using a contact-implicit whole-body optimization framework. The planner generates feasible movements without predefined contact sequences, considering the robot's full dynamics and kinematics. To plan bipedal locomotion on steps, ramps, and other terrains, we propose a mathematical model to approximate ground geometry with a smooth surface. The rigid interaction between the robot and the ground is modeled via novel contact constraints, extending the domain of applicability from flat and horizontal surfaces to any arbitrary smooth surface. Effectiveness is demonstrated using nonlinear programming to plan motions on various terrain topologies. We also explore dynamic trajectory generation by embedding high-level requirements in the cost function and the initial guess. Preliminary feasibility tests were conducted over non-coplanar terrains, both in simulation and on the real robot ErgoCub.
Abstract:This letter presents a trajectory planner for humanoid robots to perform dynamic motions on complex, parameterizable terrains using a contact-implicit whole-body optimization framework. The planner generates feasible movements without predefined contact sequences, considering the robot's full dynamics and kinematics. To plan bipedal locomotion on steps, ramps, and other terrains, we propose a mathematical model to approximate ground geometry with a smooth surface. The rigid interaction between the robot and the ground is modeled via novel contact constraints, extending the domain of applicability from flat and horizontal surfaces to any arbitrary smooth surface. Effectiveness is demonstrated using nonlinear programming to plan motions on various terrain topologies. We also explore dynamic trajectory generation by embedding high-level requirements in the cost function and the initial guess. Preliminary feasibility tests were conducted over non-coplanar terrains, both in simulation and on the real robot ErgoCub.
Author-corrected version of the article published in IEEE Robotics and Automation Letters, vol. 10, no. 11, pp. 11674-11681, November 2025. Typos corrected in Eqs. (7)-(8), with minor textual clarifications. Implementation and results unchanged
Robotics (cs.RO)
arXiv:2611.05585 [cs.RO]
(or arXiv:2611.05585v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2611.05585 arXiv-issued DOI via DataCite (pending registration)
IEEE Robotics and Automation Letters, vol. 10, no. 11, pp. 11674-11681, November 2025
https://doi.org/10.1109/LRA.2025.3614066 DOI(s) linking to related resources
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