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.
In order to make CITO numerically more tractable without relaxations, @cite_3 proposed a direct method with complementarity constraints based on the time-stepping scheme initially proposed in @cite_30 . @cite_28 use such a method for grasping and dexterous manipulation but with complementarity constraints-based contact models developed for manipulation problems. In order to improve convergence, @cite_2 relaxes the complementarity constraints; while @cite_4 and @cite_6 propose hierarchical approaches to warm start the optimization subject to strict complementarity constraints. @cite_5 recently proposed another direct method (without complementarity constraints) based on a continuous parameterization of feet motion and forces to generate gait sequences. Direct methods have successfully obtained highly-dynamic, complex motions, yet they are typically not applicable for real-time applications.
@cite_30 @cite_4 @cite_28 @cite_3 @cite_6 @cite_2 @cite_5
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Traditional motion planning approaches for multilegged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or nonconvex optimization with intractable computation time. In this letter, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions, and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a prespecified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where nonconvexity and flat terrain assumptions might lead to suboptimal or unstable plans. Our method increases the motion robustness while keeping a low computation time. 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. We present a method for smoothing discontinuous dynamics involving contact and friction, thereby facilitating the use of local optimization techniques for control. The method replaces the standard Linear Complementarity Problem with a Stochastic Linear Complementarity Problem. The resulting dynamics are continuously differentiable, and the resulting controllers are robust to disturbances. We demonstrate our method on a simulated 6-dimensional manipulation task, which involves a finger learning to spin an anchored object by repeated flicking. 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.