Retargeting human kinematic reference motion onto a robot's morphology remains a formidable challenge. Existing methods often produce physical inconsistencies, such as foot sliding, self-collisions, or dynamically infeasible motions, which hinder downstream imitation learning. We propose a bilevel optimization framework that jointly adapts reference motions to a robot's morphology while training a tracking policy using reinforcement learning. To make the optimization tractable, we derive an approximate gradient for the upper-level loss. Our framework requires only a sparse set of semantic rigid-body correspondences and eliminates the need for manual tuning by identifying optimal values for a parameterization expressive enough to preserve characteristic motion across different embodiments. Moreover, by integrating retargeting directly with physics simulation, we produce physically plausible motions that facilitate robust imitation learning. We validate our method in simulation and on hardware, demonstrating challenging motions for morphologies that differ significantly from a human, including retargeting onto a quadruped.

Teleoperated robotic characters can perform expressive interactions with humans, relying on the operators’ experience and social intuition. In this work, we propose to create autonomous interactive robots, by training a model to imitate operator data. Our model is trained on a dataset of human-robot interactions, where an expert operator is asked to vary the interactions and mood of the robot, while the operator commands as well as the pose of the human and robot are recorded. Our approach learns to predict continuous operator commands through a diffusion process and discrete commands through a classifier, all unified within a single transformer architecture. We evaluate the resulting model in simulation and with a user study on the real system. We show that our method enables simple autonomous human-robot interactions that are comparable to the expert-operator baseline, and that users can recognize the different robot moods as generated by our model. Finally, we demonstrate a zero-shot transfer of our model onto a different robotic platform with the same operator interface.

We present a constrained Rigid Body Dynamics (RBD) that guarantees satisfaction of kinematic constraints, enabling direct simulation of complex mechanical systems with arbitrary kinematic structures. To ensure constraint satisfaction, we use an implicit integration scheme. For this purpose, we derive compatible dynamic equations expressed through the quaternion time derivative, adopting an additive approach to quaternion updates instead of a multiplicative one, while enforcing quaternion unit-length as a constraint. We support all joints between rigid bodies that restrict subsets of the three translational or three rotational degrees of freedom, including position- and force-based actuation. Their constraints are formulated such that Lagrange multipliers are interpretable as joint forces and torques. We discuss a unified solution strategy for systems with redundant constraints, overactuation, and passive degrees of freedom, by eliminating redundant constraints and navigating the subspaces spanned by multipliers. As our method uses a standard additive update, we can interface with unconditionally-stable implicit integrators. Moreover, the simulation can readily be made differentiable as we show with examples.

Abstract Recent progress in physics‐based character control has made it possible to learn policies from unstructured motion data. However, it remains challenging to train a single control policy that works with diverse and unseen motions, and can be deployed to real‐world physical robots. In this paper, we propose a two‐stage technique that enables the control of a character with a full‐body kinematic motion reference, with a focus on imitation accuracy. In a first stage, we extract a latent space encoding by training a variational autoencoder, taking short windows of motion from unstructured data as input. We then use the embedding from the time‐varying latent code to train a conditional policy in a second stage, providing a mapping from kinematic input to dynamics‐aware output. By keeping the two stages separate, we benefit from self‐supervised methods to get better latent codes and explicit imitation rewards to avoid mode collapse. We demonstrate the efficiency and robustness of our method in simulation, with unseen user‐specified motions, and on a bipedal robot, where we bring dynamic motions to the real world.

Procedural animation has seen widespread use in the design of expressive walking gaits for virtual characters. While similar tools could breathe life into robotic characters, existing techniques are largely unaware of the kinematic and dynamic constraints imposed by physical robots. In this paper, we propose a system for the artist-directed authoring of stylized bipedal walking gaits, tailored for execution on robotic characters. The artist interfaces with an interactive editing tool that generates the desired character motion in realtime, either on the physical or simulated robot, using a model-based control stack. Each walking style is encoded as a set of sample parameters which are translated into whole-body reference trajectories using the proposed procedural animation technique. In order to generalize the stylized gait over a continuous range of input velocities, we employ a phase-space blending strategy that interpolates a set of example walk cycles authored by the animator while preserving contact constraints. To demonstrate the utility of our approach, we animate gaits for a custom, free-walking robotic character, and show, with two additional in-simulation examples, how our procedural animation technique generalizes to bipeds with different degrees of freedom, proportions, and mass distributions.

Legged robots are designed to perform highly dynamic motions. However, it remains challenging for users to retarget expressive motions onto these complex systems. In this paper, we present a Differentiable Optimal Control (DOC) framework that facilitates the transfer of rich motions from either animals or animations onto these robots. Interfacing with either motion capture or animation data, we formulate retargeting objectives whose parameters make them agnostic to differences in proportions and numbers of degrees of freedom between input and robot. Optimizing these parameters over the manifold spanned by optimal state and control trajectories, we minimize the retargeting error. We demonstrate the utility and efficacy of our modeling by applying DOC to a Model-Predictive Control (MPC) formulation, showing retargeting results for a family of robots of varying proportions and mass distribution. With a hardware deployment, we further show that the retargeted motions are physically feasible, while MPC ensures that the robots retain their capability to react to unexpected disturbances.

The kinematic motion of a robotic character is defined by its mechanical joints and actuators that restrict the relative motion of its rigid components. Designing robots that perform a given target motion as closely as possible with a fixed number of actuated degrees of freedom is challenging, especially for robots that form kinematic loops. In this paper, we propose a technique that simultaneously solves for optimal design and control parameters for a robotic character whose design is parameterized with configurable joints. At the technical core of our technique is an efficient solution strategy that uses dynamic programming to solve for optimal state, control, and design parameters, together with a strategy to remove redundant constraints that commonly exist in general robot assemblies with kinematic loops. We demonstrate the efficacy of our approach by either editing the design of an existing robotic character, or by optimizing the design of a new character to perform a desired motion.

This article introduces a computational approach for routing thin artificial muscle actuators through hyperelastic soft robots, in order to achieve a desired deformation behavior. Provided with a robot design and a set of example deformations, we continuously co-optimize the routing of actuators, and their actuation, to approximate example deformations as closely as possible. We introduce a data-driven model for McKibben muscles, modeling their contraction behavior when embedded in a silicone elastomer matrix. To enable the automated routing, a differentiable hyperelastic material simulation is presented. Because standard finite elements are not differentiable at element boundaries, we implement a moving least squares formulation, making the deformation gradient twice differentiable. Our robots are fabricated in a two-step molding process, with the complex mold design steps automated. While most soft robotic designs utilize bending, we study the use of our technique in approximating twisting deformations on a bar example. To demonstrate the efficacy of our technique in soft robotic design, we show a continuum robot, a tentacle, and a four-legged walking robot.

This paper presents a novel design for a large-scale interactive tactile display. Fast dynamic tactile effects are created at high spatial resolution on a flexible screen, using directable nozzles that spray water jets onto the rear of the screen. The screen further has back-projected visual content and touch interaction. The technology is demonstrated in Feeling Fireworks, a tactile firework show. The goal is to make fireworks more inclusive for the Blind and Low-Vision (BLV) community. A BLV focus group provided input during the development process, and a user study with BLV users showed that Feeling Fireworks is an enjoyable and meaningful experience. A user study with sighted users showed that users could accurately label the correspondence between the designed tactile firework effects and corresponding visual fireworks. Beyond the Feeling Fireworks application, this is a novel approach for scalable tactile displays with potential for broader use.

We present a system for fast and robust handovers with a robot character, together with a user study investigating the effect of robot speed and reaction time on perceived interaction quality. The system can match and exceed human speeds and confirms that users prefer human-level timing. The system has the appearance of a robot character, with a bear-like head and a soft anthropomorphic hand and uses Bézier curves to achieve smooth minimum-jerk motions. Fast timing is enabled by low latency motion capture and real-time trajectory generation: the robot initially moves towards an expected handover location and the trajectory is updated on-the-fly to converge smoothly to the actual handover location. A hybrid automaton provides robustness to failure and unexpected human actions. In a 3x3 user study, we vary the speed of the robot and add variable sensorimotor delays. We evaluate the social perception of the robot using the Robot Social Attribute Scale (RoSAS). Inclusion of a small delay, mimicking the delay of the human sensorimotor system, leads to an improvement in perceived qualities over both no delay and long delay conditions. Specifically, with no delay the robot is perceived as more discomforting, and with a long delay it is perceived as less warm.

We propose a novel generic shape optimization method for CAD models based on the eXtended Finite Element Method (XFEM). Our method works directly on the intersection between the model and a regular simulation grid, without the need to mesh or remesh, thus removing a bottleneck of classical shape optimization strategies. This is made possible by a novel hierarchical integration scheme that accurately integrates finite element quantities with sub-element precision. For optimization, we efficiently compute analytical shape derivatives of the entire framework, from model intersection to integration rule generation and XFEM simulation. Moreover, we describe a differentiable projection of shape parameters onto a constraint manifold spanned by user-specified shape preservation, consistency, and manufacturability constraints. We demonstrate the utility of our approach by optimizing mass distribution, strength-to-weight ratio, and inverse elastic shape design objectives directly on parameterized 3D CAD models.

Creating animations for robotic characters is very challenging due to the constraints imposed by their physical nature. In particular, the combination of fast motions and unavoidable structural deformations leads to mechanical oscillations that negatively affect their performances. Our goal is to automatically transfer motions created using traditional animation software to robotic characters while avoiding such artifacts. To this end, we develop an optimization-based, dynamics-aware motion retargeting system that adjusts an input motion such that visually salient low-frequency, large amplitude vibrations are suppressed. The technical core of our animation system consists of a differentiable dynamics simulator that provides constraint-based two-way coupling between rigid and flexible components. We demonstrate the efficacy of our method through experiments performed on a total of five robotic characters including a child-sized animatronic figure that features highly dynamic drumming and boxing motions.

Elastically deforming wire structures are lightweight, durable, and can be bent within minutes using CNC bending machines. We present a computational technique for the design of kinetic wire characters, tailored for fabrication on consumer-grade hardware. Our technique takes as input a network of curves or a skeletal animation, then estimates a cable-driven, compliant wire structure which matches user-selected targets or keyframes as closely as possible. To enable large localized deformations, we shape wire into functional spring-like entities at a discrete set of locations. We first detect regions where changes to local stiffness properties are needed, then insert bendable entities of varying shape and size. To avoid a discrete optimization, we first optimize stiffness properties of generic, non-fabricable entities which capture well the behavior of our bendable designs. To co-optimize stiffness properties and cable forces, we formulate an equilibrium-constrained minimization problem, safeguarding against inelastic deformations. We demonstrate our method on six fabricated examples, showcasing rich behavior including large deformations and complex, spatial motion.

Handshakes are common greetings, and humans therefore have strong priors of what a handshake should feel like. This makes it challenging to create compelling and realistic human-robot handshakes, necessitating the consideration of human haptic perception in the design of robot hands. At its most basic level, haptic perception is encoded by contact points and contact pressure distributions on the skin. This motivates our work on measuring the contact area and contact pressure in human handshaking interactions. We present two benchmarking experiments in this regard, measuring the contact locations in human-human/human-robot handshaking and the contact pressure distribution for handshakes with a sensorized palm. We present results from human studies with the benchmarking experiments, providing a baseline for comparison with robot hands as well as presenting new insights into human handshaking. We also show initial work in using these results for the evaluation of robot hands, and progressing towards iterative design of robot hands optimized for social hand interactions.

We present a method for designing and fabricating MetaSilicones ---composite silicone rubbers that exhibit desired macroscopic mechanical properties. The underlying principle of our approach is to inject spherical inclusions of a liquid dopant material into a silicone matrix material. By varying the number, size, and locations of these inclusions as well as their material, a broad range of mechanical properties can be achieved. The technical core of our approach is formed by an optimization algorithm that, combining a simulation model based on extended finite elements (XFEM) and sensitivity analysis, computes inclusion distributions that lead to desired stiffness properties on the macroscopic level. We explore the design space of MetaSilicone on an extensive set of simulation experiments involving materials with optimized uni- and bi-directional stiffness, spatially-graded properties, as well as multi-material composites. We present validation through standard measurements on physical prototypes, which we fabricate on a modified filament-based 3D printer, thus combining the advantages of digital fabrication with the mechanical performance of silicone elastomers.

Tactile force sensing and compliance are key elements of safe and natural-feeling human-robot interaction. We present an optical tactile sensor in the form of a compliant elastomer 'fingertip' tracked by a high-speed low-resolution image sensor with on-board signal processing. We propose a dual-mode bio-mimetic control loop, where in reflex mode the sensor sends fast reflexive action commands directly to actuators, bypassing the central controller to minimise reaction times. For higher-level interpretation, a slower explore mode enables more sophisticated processing of the sensory input by the central controller. We demonstrate sensing of normal force in both modes of operation, showing that in reflex mode we are able to rapidly detect the presence of forces and compute an approximate magnitude estimate while in explore mode we are able to perform more accurate force measurements.