The Indirect Method for Generating Libraries of Optimal Periodic Trajectories and Its Application to Economical Bipedal Walking
arXiv:2410.09512v2 Announce Type: replace Abstract: Trajectory optimization is an essential tool for generating efficient, dynamically consistent gaits in legged locomotion. This paper explores the indirect method of trajectory optimization, emphasizing its application in creating optimal periodic gaits for legged systems and contrasting it with the more common direct method. While the direct method provides flexibility in implementation, it is limited by its need for an input space parameterization. In contrast, the indirect method improves accuracy by computing the control input from states and costates obtained along the optimal trajectory. In this work, we tackle the convergence challenges associated with indirect shooting methods by utilizing numerical continuation methods. This is pa
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Abstract:Trajectory optimization is an essential tool for generating efficient, dynamically consistent gaits in legged locomotion. This paper explores the indirect method of trajectory optimization, emphasizing its application in creating optimal periodic gaits for legged systems and contrasting it with the more common direct method. While the direct method provides flexibility in implementation, it is limited by its need for an input space parameterization. In contrast, the indirect method improves accuracy by computing the control input from states and costates obtained along the optimal trajectory. In this work, we tackle the convergence challenges associated with indirect shooting methods by utilizing numerical continuation methods. This is particularly useful for the systematic development of gait libraries. Our contributions include: (1) the formalization of a general periodic trajectory optimization problem that extends existing first-order necessary conditions to a broader range of cost functions and operating conditions; (2) a methodology for efficiently generating libraries of optimal trajectories (gaits) utilizing a single shooting approach combined with numerical continuation methods; (3) a novel approach for reconstructing Lagrange multipliers and costates from passive gaits; (4) a comparative analysis of the indirect and direct shooting methods using a compass-gait walker as a case study, demonstrating the improved accuracy of the indirect method in generating optimal gaits; and (5) demonstrating applicability to the more complex legged robot RABBIT, with ten dynamic states and four inputs. The findings underscore the potential of the indirect method for generating families of optimal gaits, thereby advancing the field of trajectory optimization in legged robotics.
Comments: submitted to the International Journal of Robotics Research (IJRR)
Subjects:
Robotics (cs.RO)
Cite as: arXiv:2410.09512 [cs.RO]
(or arXiv:2410.09512v2 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2410.09512
arXiv-issued DOI via DataCite
Submission history
From: Maximilian Raff [view email] [v1] Sat, 12 Oct 2024 12:22:05 UTC (456 KB) [v2] Wed, 1 Apr 2026 12:52:38 UTC (2,449 KB)
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