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