ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.Comment: Moritz Geilinger and David Hahn contributed equally to this wor

An adaptive framework for changing-contact robot manipulation

Many robot manipulation tasks require the robot to make and break contact with other objects in the environment. The interaction dynamics of such tasks vary markedly before and after contact. They are also strongly influenced by the nature and physical properties of the objects involved, i.e., by factors such as type of contact, surface friction, and applied force. Many industrial assembly tasks and human manipulation tasks, e.g., peg insertion, stacking, and screwing, are instances of such `changing-contact' manipulation tasks. In such tasks, the interaction dynamics is discontinuous when the robot makes or breaks contact but smooth at other times, making it a piecewise continuous dynamical system. The discontinuities experienced by a robot during such tasks can be harmful to the robot and/or object. Designing a framework for smooth online control of changing-contact manipulation tasks is a challenging open problem. To complete any manipulation task without data-intensive pre-training, the robot has to plan a motion trajectory, and execute this trajectory accurately and smoothly. Many methods have been developed for the former part of the problem in the form of planners that compute a suitable trajectory while considering relevant motion constraints and environmental obstacles. This thesis focuses on the relatively less-explored latter (i.e., plan execution) part of the problem in the context of changing-contact manipulation tasks. It does so by developing an adaptive, task-space, hybrid control framework that enables efficient, smooth, and accurate following of any given motion trajectory in the presence of piecewise continuous interaction dynamics. The framework makes three key contributions. The first contribution of this thesis addresses the problem of controlling a robot performing continuous-contact tasks in the presence of smoothly-changing environment dynamics. Specifically, we provide a task-space control framework that incrementally models and predicts the end-effector wrenches, and uses the discrepancies between the predicted and measured values to revise the predictive (forward) model and to achieve smooth trajectory tracking by adapting the impedance parameters of a force-motion controller. The second contribution of the thesis expands our framework to handle interaction dynamics that can be discontinuous due to making and breaking of contacts or due to discrete changes in the environment. We formulate the piecewise continuous interaction dynamics of the robot as a hybrid dynamical system with previously unknown discrete dynamic modes. We propose a corresponding hybrid framework that incrementally identifies new or existing modes, and adapts the parameters of the dynamics models within each such mode to provide smooth and accurate tracking of the target motion trajectory. The third contribution of the thesis focuses on handling contact changes and reducing discontinuities in the interaction dynamics during mode transitions. Specifically, we develop a framework with a contact anticipation model that incrementally and probabilistically updates its estimates of when contact changes occur due to making or breaking contact, or changes in the properties of objects. The estimated contact positions are used to guide a transition to (and from) special `transition phase' controllers whose parameters are adapted online to minimise discontinuities (i.e., to minimise spikes in force, jerk etc) in the regions of anticipated contacts. The stated contributions and each part of the framework are grounded and evaluated in simulation and on a physical robot performing illustrative changing-contact manipulation tasks on a tabletop. We experimentally compare our framework with some baselines to demonstrate the importance of building an incremental, adaptive framework for such tasks. In particular, we compare our controller for continuous-contact tasks with representative baselines in the adaptive control literature, and demonstrate the benefits of an incrementally-updated predictive (forward) model. We also experimentally evaluate the ability of our hybrid framework to accurately identify and model the dynamics of discrete dynamic (contact) modes, and justify the need for online updates by comparing the performance of a state of the art offline methods for hybrid dynamical systems. Finally, we evaluate the ability of our framework to accurately estimate contact positions and minimise discontinuities in the interaction dynamics in motion trajectories involving multiple contact changes

Analysis and synthesis of bipedal humanoid movement : a physical simulation approach

textAdvances in graphics and robotics have increased the importance of tools for synthesizing humanoid movements to control animated characters and physical robots. There is also an increasing need for analyzing human movements for clinical diagnosis and rehabilitation. Existing tools can be expensive, inefficient, or difficult to use. Using simulated physics and motion capture to develop an interactive virtual reality environment, we capture natural human movements in response to controlled stimuli. This research then applies insights into the mathematics underlying physics simulation to adapt the physics solver to support many important tasks involved in analyzing and synthesizing humanoid movement. These tasks include fitting an articulated physical model to motion capture data, modifying the model pose to achieve a desired configuration (inverse kinematics), inferring internal torques consistent with changing pose data (inverse dynamics), and transferring a movement from one model to another model (retargeting). The result is a powerful and intuitive process for analyzing and synthesizing movement in a single unified framework.Computer Science

Optimization-Based Control for Dynamic Legged Robots

In a world designed for legs, quadrupeds, bipeds, and humanoids have the opportunity to impact emerging robotics applications from logistics, to agriculture, to home assistance. The goal of this survey is to cover the recent progress toward these applications that has been driven by model-based optimization for the real-time generation and control of movement. The majority of the research community has converged on the idea of generating locomotion control laws by solving an optimal control problem (OCP) in either a model-based or data-driven manner. However, solving the most general of these problems online remains intractable due to complexities from intermittent unidirectional contacts with the environment, and from the many degrees of freedom of legged robots. This survey covers methods that have been pursued to make these OCPs computationally tractable, with specific focus on how environmental contacts are treated, how the model can be simplified, and how these choices affect the numerical solution methods employed. The survey focuses on model-based optimization, covering its recent use in a stand alone fashion, and suggesting avenues for combination with learning-based formulations to further accelerate progress in this growing field.Comment: submitted for initial review; comments welcom