There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Origami can turn a sheet of paper into complex three-dimensional shapes, and similar folding techniques can produce structures and mechanisms. To demonstrate the application of these techniques to the fabrication of machines, we developed a crawling robot that folds itself. The robot starts as a flat sheet with embedded electronics, and transforms autonomously into a functional machine. To accomplish this, we developed shape-memory composites that fold themselves along embedded hinges. We used these composites to recreate fundamental folded patterns, derived from computational origami, that can be extrapolated to a wide range of geometries and mechanisms. This origami-inspired robot can fold itself in 4 minutes and walk away without human intervention, demonstrating the potential both for complex self-folding machines and autonomous, self-controlled assembly.

/pdf/a-method-for-building-self-folding-machines-57agl8pynh.pdf

A method for building self-folding machines

Legged robots pose one of the greatest challenges in robotics. Dynamic and agile maneuvers of animals cannot be imitated by existing methods that are crafted by humans. A compelling alternative is reinforcement learning, which requires minimal craftsmanship and promotes the natural evolution of a control policy. However, so far, reinforcement learning research for legged robots is mainly limited to simulation, and only few and comparably simple examples have been deployed on real systems. The primary reason is that training with real robots, particularly with dynamically balancing systems, is complicated and expensive. In the present work, we introduce a method for training a neural network policy in simulation and transferring it to a state-of-the-art legged system, thereby leveraging fast, automated, and cost-effective data generation schemes. The approach is applied to the ANYmal robot, a sophisticated medium-dog-sized quadrupedal system. Using policies trained in simulation, the quadrupedal machine achieves locomotion skills that go beyond what had been achieved with prior methods: ANYmal is capable of precisely and energy-efficiently following high-level body velocity commands, running faster than before, and recovering from falling even in complex configurations.

/pdf/learning-agile-and-dynamic-motor-skills-for-legged-robots-41hdxn2m1m.pdf

Learning agile and dynamic motor skills for legged robots

Inspired by how humans learn dynamic motor skills through a progressive process of coaching and practices, we introduce an intuitive and interactive framework for developing dynamic controllers. The user only needs to provide a primitive initial controller and high-level, human-readable instructions as if s/he is coaching a human trainee, while the character has the ability to interpret the abstract instructions, accumulate the knowledge from the coach, and improve its skill iteratively. We introduce “control rigs” as an intermediate layer of control module to facilitate the mapping between high-level instructions and low-level control variables. Control rigs also utilize the human coach's knowledge to reduce the search space for control optimization. In addition, we develop a new sampling-based optimization method, Covariance Matrix Adaptation with Classification (CMA-C), to efficiently compute-control rig parameters. Based on the observation of human ability to “learn from failure”, CMA-C utilizes the failed simulation trials to approximate an infeasible region in the space of control rig parameters, resulting a faster convergence for the CMA optimization. We demonstrate the design process of complex dynamic controllers using our framework, including precision jumps, turnaround jumps, monkey vaults, drop-and-rolls, and wall-backflips.

Iterative Training of Dynamic Skills Inspired by Human Coaching Techniques

Legged locomotion can extend the operational domain of robots to some of the most challenging environments on Earth. However, conventional controllers for legged locomotion are based on elaborate state machines that explicitly trigger the execution of motion primitives and reflexes. These designs have increased in complexity but fallen short of the generality and robustness of animal locomotion. Here, we present a robust controller for blind quadrupedal locomotion in challenging natural environments. Our approach incorporates proprioceptive feedback in locomotion control and demonstrates zero-shot generalization from simulation to natural environments. The controller is trained by reinforcement learning in simulation. The controller is driven by a neural network policy that acts on a stream of proprioceptive signals. The controller retains its robustness under conditions that were never encountered during training: deformable terrains such as mud and snow, dynamic footholds such as rubble, and overground impediments such as thick vegetation and gushing water. The presented work indicates that robust locomotion in natural environments can be achieved by training in simple domains.

/pdf/learning-quadrupedal-locomotion-over-challenging-terrain-197h5zrqbx.pdf

Learning quadrupedal locomotion over challenging terrain

We present an interactive design system that allows non-expert users to create animated mechanical characters. Given an articulated character as input, the user iteratively creates an animation by sketching motion curves indicating how different parts of the character should move. For each motion curve, our framework creates an optimized mechanism that reproduces it as closely as possible. The resulting mechanisms are attached to the character and then connected to each other using gear trains, which are created in a semi-automated fashion. The mechanical assemblies generated with our system can be driven with a single input driver, such as a hand-operated crank or an electric motor, and they can be fabricated using rapid prototyping devices. We demonstrate the versatility of our approach by designing a wide range of mechanical characters, several of which we manufactured using 3D printing. While our pipeline is designed for characters driven by planar mechanisms, significant parts of it extend directly to non-planar mechanisms, allowing us to create characters with compelling 3D motions.

/pdf/computational-design-of-mechanical-characters-4zf3769h1z.pdf

Computational design of mechanical characters

We present a control strategy for physically-simulated walking motions that generalizes well across gait parameters, motion styles, character proportions, and a variety of skills. The control is realtime, requires no character-specific or motion-specific tuning, is robust to disturbances, and is simple to compute. The method works by integrating tracking, using proportional-derivative control; foot placement, using an inverted pendulum model; and adjustments for gravity and velocity errors, using Jacobian transpose control. High-level gait parameters allow for forwards-and-backwards walking, various walking speeds, turns, walk-to-stop, idling, and stop-to-walk behaviors. Character proportions and motion styles can be authored interactively, with edits resulting in the instant realization of a suitable controller. The control is further shown to generalize across a variety of walking-related skills, including picking up objects placed at any height, lifting and walking with heavy crates, pushing and pulling crates, stepping over obstacles, ducking under obstacles, and climbing steps.

/pdf/generalized-biped-walking-control-5560vzpchg.pdf

Generalized biped walking control

We present a method for fabrication-oriented design of actuated deformable characters that allows a user to automatically create physical replicas of digitally designed characters using rapid manufacturing technologies. Given a deformable character and a set of target poses as input, our method computes a small set of actuators along with their locations on the surface and optimizes the internal material distribution such that the resulting character exhibits the desired deformation behavior. We approach this problem with a dedicated algorithm that combines finite-element analysis, sparse regularization, and constrained optimization. We validate our pipeline on a set of two- and three-dimensional example characters and present results in simulation and physically-fabricated prototypes.

/pdf/computational-design-of-actuated-deformable-characters-1gzdeh8nh8.pdf

Computational design of actuated deformable characters

Quadrupedal animals move through their environments with unmatched agility and grace An important part of this is the ability to choose between different gaits in order to travel optimally at a certain speed or to robustly deal with unanticipated perturbations In this paper, we present a control framework for a quadrupedal robot that is capable of locomoting using several gaits We demonstrate the flexibility of the algorithm by performing experiments on StarlETH, a recently-developed quadrupedal robot We implement controllers for a static walk, a walking trot, and a running trot, and show that smooth transitions between them can be performed Using this control strategy, StarlETH is able to trot unassisted in 3D space with speeds of up to 07m/s, it can dynamically navigate over unperceived 5-cm high obstacles and it can recover from significant external pushes

/pdf/control-of-dynamic-gaits-for-a-quadrupedal-robot-20qdfbnny3.pdf

Control of dynamic gaits for a quadrupedal robot

We present a design system for linkage-based characters, combining form and function in an aesthetically-pleasing manner. Linkage-based character design exhibits a mix of discrete and continuous problems, making for a highly unintuitive design space that is difficult to navigate without assistance. Our system significantly simplifies this task by allowing users to interactively browse different topology options, thus guiding the discrete set of choices that need to be made. A subsequent continuous optimization step improves motion quality and, crucially, safeguards against singularities. We demonstrate the flexibility of our method on a diverse set of character designs, and then realize our designs by physically fabricating prototypes.

Stelian Coros

Papers

Computational design of mechanical characters

Generalized biped walking control

Computational design of actuated deformable characters

Control of dynamic gaits for a quadrupedal robot

Computational design of linkage-based characters