In this paper, we propose a contact-implicit trajectory optimization (CITO) method based on a variable smooth contact model (VSCM) and successive convexification (SCvx). The VSCM facilitates the convergence of gradient-based optimization without compromising physical fidelity. On the other hand, the proposed SCvx-based approach combines the advantages of direct and shooting methods for CITO. For evaluations, we consider non-prehensile manipulation tasks. The proposed method is compared to a version based on iterative linear quadratic regulator (iLQR) on a planar example. The results demonstrate that both methods can find physically-consistent motions that complete the tasks without a meaningful initial guess owing to the VSCM. The proposed SCvx-based method outperforms the iLQR-based method in terms of convergence, computation time, and the quality of motions found. Finally, the proposed SCvx-based method is tested on a standard robot platform and shown to perform efficiently for a real-world application.
The main objective of contact-implicit trajectory optimization is to solve for non-smooth trajectories with impacts and discontinuities as a finite-dimensional optimization problem. For this purpose, Yunt & Glocker @cite_31 proposed transcribing such a problem into an NLP with complementarity constraints and a bilevel optimization where the control inputs are optimized at the higher level while the states and contact forces are optimized at the lower level. On the other hand, @cite_13 @cite_9 generate complex behaviors for animated characters through a shooting NLP with soft constraints that model contacts. Nevertheless, in these studies, various relaxations are made to solve an unconstrained NLP efficiently by compromising physical realism.
@cite_9 @cite_31 @cite_13
2161697934 1552665521 2042408133
We present a method for automatic synthesis of dexterous hand movements, given only high-level goals specifying what should happen to the object being manipulated. Results are presented on a wide range of tasks including grasping and picking up objects, twirling them between the fingers, tossing and catching, drawing. This work is an extension of the recent contact-invariant optimization (CIO) method, which introduced auxiliary decision variables directly specifying when and where contacts should occur, and optimized these variables together with the movement trajectory. Our contribution here is extending the unique contact model used in CIO which was specific to locomotion tasks, as well as applying the extended method systematically to hand manipulation. The aim of this report is to propose a unified framework for the determination of non-smooth trajectories for structure-variant mechanical systems along with a computational scheme. The benefits to represent the dynamics as a measure-differential inclusion are presented. The optimal control problem is transcribed into a nonlinear programming problem (NLP) and transformed from the infinite dimensional representation into a finite dimensional representation. The relation to bilevel programming is established. A numerical scheme is proposed for the determination of the state and costate trajectories, which can bear discontinuities and set-valuedness We present a motion synthesis framework capable of producing a wide variety of important human behaviors that have rarely been studied, including getting up from the ground, crawling, climbing, moving heavy objects, acrobatics (hand-stands in particular), and various cooperative actions involving two characters and their manipulation of the environment. Our framework is not specific to humans, but applies to characters of arbitrary morphology and limb configuration. The approach is fully automatic and does not require domain knowledge specific to each behavior. It also does not require pre-existing examples or motion capture data. At the core of our framework is the contact-invariant optimization (CIO) method we introduce here. It enables simultaneous optimization of contact and behavior. This is done by augmenting the search space with scalar variables that indicate whether a potential contact should be active in a given phase of the movement. These auxiliary variables affect not only the cost function but also the dynamics (by enabling and disabling contact forces), and are optimized together with the movement trajectory. Additional innovations include a continuation scheme allowing helper forces at the potential contacts rather than the torso, as well as a feature-based model of physics which is particularly well-suited to the CIO framework. We expect that CIO can also be used with a full physics model, but leave that extension for future work.