A direct method for trajectory optimization of rigid bodies through contact
Open accessAbstract
Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform.
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Legged locomotion is another area in which contact between the leg and the ground must be considered, and most robotics work that considers contact originates from legged locomotion.
“Legged locomotion is another area in which contact (between the leg and the ground) must be considered, and most of the robotics work that considers contact originates from legged locomotion (Erez et al., 2011; Posa et al., 2014; Marcucci et al., 2017; Pace and Burden, 2017; Deits et al., 2019).”
From Lessons for Robotics From the Control Architecture of the Octopus (2022) · cites this paper as Posa et al., 2014
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“Legged locomotion is another area in which contact (between the leg and the ground) must be considered, and most of the robotics work that considers contact originates from legged locomotion (Erez et al., 2011; Posa et al., 2014; Marcucci et al., 2017; Pace and Burden, 2017; Deits et al., 2019).”
Background
- Authors
- Posa, M., Cantu, C., & Tedrake, R.
- Affiliations
- Massachusetts Institute of Technology (US)
- Venue
- The International Journal of Robotics Research
- Publisher
- SAGE Publications
- Published
- 2013-10-21
- Volume
- 33
- Issue
- 1
- Pages
- 69-81
- ISSN
- 0278-3649 (ISSN-L)
- 1741-3176
- OpenAlex
- W2101340954
- Cited by
- 597
- References
- 43
- Citations by year
- 2026: 26 · 2025: 38 · 2024: 56 · 2023: 63 · 2022: 75 · 2021: 73 · 2020: 62 · 2019: 63 · 2018: 44 · 2017: 47 · 2016: 26 · 2015: 18 · 2014: 6
- FWCI
- 21.91
- Type
- journal article
- Language
- en
- Update notices
- correction (2014-05-28)
- Open access
- green
- orcid.org
- Licence
- Locations
- The International Journal of Robotics Research (publishedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc-sa)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Dynamics and Control of Mechanical Systems
- Physical Sciences › Engineering › Biomedical Engineering › Robotic Locomotion and Control
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Robotic Path Planning Algorithms
- Keywords
- trajectory optimization, rigid body dynamics, contact, inelastic collisions, Coulomb friction, linear complementarity problem, sequential quadratic programming, robotic manipulation, grasping, bipedalism, bipedal running
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