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

Differentiable Dynamics and Motion Synthesis for Legged Robots

The generation of agile and dynamic motions for legged robots has long been of interest in the fields of computer graphics and robotics. However, planning motions to control these underactuated, nonlinear dynamical systems has proven to be a difficult problem. Building on recent advances in differentiable physical models and trajectory optimization, this thesis presents several approaches to synthesizing motion controls for robots with legs and wheels, as well as compliant robots. We begin by introducing a computational framework for motion gen- eration of legged-wheeled robots. The user can easily design a robotic creature with an arbitrary arrangement of legs, motor joints, and various types of end effectors, such as point feet, actuated and unactuated wheels. Once the robot’s morphology is determined, the user can create and edit motion targets, such as way points, using an interactive tool, while our tra- jectory optimization method generates physically valid motion trajectories. Finally, we fabricate prototypes designed with our system and show that the generated motions can be applied to the real world. Next, we extend our system with a warm start technique that dramatically improves the convergence rate of the trajectory optimization. Using our computational framework, we design and build an agile robot with legs and wheels, AgileBot, which can be equipped with actuated wheels, roller- blades or ice-skates. Our trajectory optimization generates various agile motions, such as roll-walking, swizzling or skating, which are executed on the physical prototype. Finally, we use our system to generate several dynamic motions as reference trajectories for feedback control of a legged- wheeled robot. Lastly, we introduce a differentiable physics engine capable of handling frictional contact for rigid and deformable objects in a unified framework. We combine a smoothed contact model with implicit time integration and sensitivity analysis to analytically compute derivatives with respect to the simulation parameters. We use our differentiable simulation to perform trajectory optimization that accounts for the full dynamics of a legged robot with compliant actuators and soft feet. We also demonstrate applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robot manipulations, and efficient self-supervised learning of control policies

Offline motion libraries and online MPC for advanced mobility skills

We describe an optimization-based framework to perform complex locomotion skills for robots with legs and wheels. The generation of complex motions over a long-time horizon often requires offline computation due to current computing constraints and is mostly accomplished through trajectory optimization (TO). In contrast, model predictive control (MPC) focuses on the online computation of trajectories, robust even in the presence of uncertainty, albeit mostly over shorter time horizons and is prone to generating nonoptimal solutions over the horizon of the task's goals. Our article's contributions overcome this trade-off by combining offline motion libraries and online MPC, uniting a complex, long-time horizon plan with reactive, short-time horizon solutions. We start from offline trajectories that can be, for example, generated by TO or sampling-based methods. Also, multiple offline trajectories can be composed out of a motion library into a single maneuver. We then use these offline trajectories as the cost for the online MPC, allowing us to smoothly blend between multiple composed motions even in the presence of discontinuous transitions. The MPC optimizes from the measured state, resulting in feedback control, which robustifies the task's execution by reacting to disturbances and looking ahead at the offline trajectory. With our contribution, motion designers can choose their favorite method to iterate over behavior designs offline without tuning robot experiments, enabling them to author new behaviors rapidly. Our experiments demonstrate complex and dynamic motions on our traditional quadrupedal robot ANYmal and its roller-walking version. Moreover, the article's findings contribute to evaluating five planning algorithms.ISSN:0278-3649ISSN:1741-317