Contact-Implicit Trajectory Optimization Based on a Variable Smooth Contact Model and Successive Convexification

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.Comment: Accepted for publication in ICRA 201

A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward initialization and a closed-loop forward integration. All algorithms have similar computational complexity, i.e. linear complexity in the time horizon, and can be derived in the same computational framework. We compare the full-step variants of our algorithms and present several simulation examples, including a high-dimensional underactuated robot subject to contact switches. Simulation results show that our multiple-shooting algorithms can achieve faster convergence, better local contraction rates and much shorter runtimes than classical iLQR, which makes them a superior choice for nonlinear model predictive control applications.Comment: 8 page

Learning a Structured Neural Network Policy for a Hopping Task

In this work we present a method for learning a reactive policy for a simple dynamic locomotion task involving hard impact and switching contacts where we assume the contact location and contact timing to be unknown. To learn such a policy, we use optimal control to optimize a local controller for a fixed environment and contacts. We learn the contact-rich dynamics for our underactuated systems along these trajectories in a sample efficient manner. We use the optimized policies to learn the reactive policy in form of a neural network. Using a new neural network architecture, we are able to preserve more information from the local policy and make its output interpretable in the sense that its output in terms of desired trajectories, feedforward commands and gains can be interpreted. Extensive simulations demonstrate the robustness of the approach to changing environments, outperforming a model-free gradient policy based methods on the same tasks in simulation. Finally, we show that the learned policy can be robustly transferred on a real robot.Comment: IEEE Robotics and Automation Letters 201

Legged Robots

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A Comparative Analysis of Contact Models in Trajectory Optimization for Manipulation

In this paper, we analyze the effects of contact models on contact-implicit trajectory optimization for manipulation. We consider three different approaches: (1) a contact model that is based on complementarity constraints, (2) a smooth contact model, and our proposed method (3) a variable smooth contact model. We compare these models in simulation in terms of physical accuracy, quality of motions, and computation time. In each case, the optimization process is initialized by setting all torque variables to zero, namely, without a meaningful initial guess. For simulations, we consider a pushing task with varying complexity for a 7 degrees-of-freedom robot arm. Our results demonstrate that the optimization based on the proposed variable smooth contact model provides a good trade-off between the physical fidelity and quality of motions at the cost of increased computation time.Comment: 6 pages, 7 figures, 4 tables, IROS 2018 camera-ready versio