Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complementary strategies. First, we develop a matrix-free update step that uses Jacobian-vector products, iterative linear solvers, and stochastic covariance estimation to enable linear scaling, all while retaining stability. Second, we propose iterative re-linearization to further improve stability without sacrificing scalability, turning probabilistic ODE solvers into fully implicit methods. We evaluate the proposed approaches on a range of stiff and high-dimensional problems and demonstrate improved stability and scalability over established probabilistic solvers.

Reinforcement learning (RL) algorithms often require a large number of data samples to learn a control policy. As a result, training them directly on the real-world systems is expensive and potentially dangerous.

Our muscles are nature's actuators. The sinewy tissue is what generates the forces that make our bodies move. In recent years, engineers have used real muscle tissue to actuate "biohybrid robots" made from both living tissue and synthetic parts. By pairing lab-grown muscles with synthetic skeletons, researchers are engineering a menagerie of muscle-powered crawlers, walkers, swimmers, and grippers. But for the most part, these designs are limited in the amount of motion and power they can produce.

We introduce Guided Harmonic Path-Integral Diffusion (GH-PID), a linearly-solvable framework for guided Stochastic Optimal Transport (SOT) with a hard terminal distribution and soft, application-driven path costs. A low-dimensional guidance protocol shapes the trajectory ensemble while preserving analytic structure: the forward and backward Kolmogorov equations remain linear, the optimal score admits an explicit Green-function ratio, and Gaussian-Mixture Model (GMM) terminal laws yield closed-form expressions. This enables stable sampling and differentiable protocol learning under exact terminal matching. We develop guidance-centric diagnostics -- path cost, centerline adherence, variance flow, and drift effort -- that make GH-PID an interpretable variational ansatz for empirical SOT. Three navigation scenarios illustrated in 2D: (i) Case A: hand-crafted protocols revealing how geometry and stiffness shape lag, curvature effects, and mode evolution; (ii) Case B: single-task protocol learning, where a PWC centerline is optimized to minimize integrated cost; (iii) Case C: multi-expert fusion, in which a commander reconciles competing expert/teacher trajectories and terminal beliefs through an exact product-of-experts law and learns a consensus protocol. Across all settings, GH-PID generates geometry-aware, trust-aware trajectories that satisfy the prescribed terminal distribution while systematically reducing integrated cost.

Adaptive morphogenetic robots adapt their morphology and control policies to meet changing tasks and environmental conditions. Many such systems leverage soft components, which enable shape morphing but also introduce simulation and control challenges. Soft-body simulators remain limited in accuracy and computational tractability, while rigid-body simulators cannot capture soft-material dynamics. Here, we present a surrogate compliance modeling approach: rather than explicitly modeling soft-body physics, we introduce indirect variables representing soft-material deformation within a rigid-body simulator. We validate this approach using our amphibious robotic turtle, a quadruped with soft morphing limbs designed for multi-environment locomotion. By capturing deformation effects as changes in effective limb length and limb center of mass, and by applying reinforcement learning with extensive randomization of these indirect variables, we achieve reliable policy learning entirely in a rigid-body simulation. The resulting gaits transfer directly to hardware, demonstrating high-fidelity sim-to-real performance on hard, flat substrates and robust, though lower-fidelity, transfer on rheologically complex terrains. The learned closed-loop gaits exhibit unprecedented terrestrial maneuverability and achieve an order-of-magnitude reduction in cost of transport compared to open-loop baselines. Field experiments with the robot further demonstrate stable, multi-gait locomotion across diverse natural terrains, including gravel, grass, and mud.

This study investigates whether adding ground compliance to visual feedback (VF) gait training is more effective at increasing push-off force (POF) compared to using VF alone, with implications for gait rehabilitation. Ten healthy participants walked on a custom split-belt treadmill. All participants received real-time visual feedback of their ground reaction forces. One group also experienced changes in ground compliance, while a control group received only visual feedback. Intentional increases in propulsive ground reaction forces (POF) were successfully achieved and sustained post-intervention, especially in the group that experienced ground compliance. This group also demonstrated lasting after-effects in muscle activity and joint kinematics, indicating a more robust learning of natural strategies to increase propulsion. This work demonstrates how visual and proprioceptive systems coordinate during gait adaptation. It uniquely shows that combining ground compliance with visual feedback enhances the learning of propulsive forces, supporting the potential use of compliant terrain in long-term rehabilitation targeting propulsion deficits, such as those following a stroke.

Walking on compliant terrain presents a substantial challenge for individuals with lower-limb amputation, further elevating their already high risk of falling. While powered ankle-foot prostheses have demonstrated adaptability across speeds and rigid terrains, control strategies optimized for soft or compliant surfaces remain underexplored. This work experimentally validates an admittance-based control strategy that dynamically adjusts the quasi-stiffness of powered prostheses to enhance gait stability on compliant ground. Human subject experiments were conducted with three healthy individuals walking on two bilaterally compliant surfaces with ground stiffness values of 63 and 25 kN/m, representative of real-world soft environments. Controller performance was quantified using phase portraits and two walking stability metrics, offering a direct assessment of fall risk. Compared to a standard phase-variable controller developed for rigid terrain, the proposed admittance controller consistently improved gait stability across all compliant conditions. These results demonstrate the potential of adaptive, stability-aware prosthesis control to reduce fall risk in real-world environments and advance the robustness of human-prosthesis interaction in rehabilitation robotics.

Continuum manipulators offer intrinsic dexterity and safe geometric compliance for navigation within confined and obstacle-rich environments. However, their infinite-dimensional backbone deformation, unmodeled internal friction, and configuration-dependent stiffness fundamentally limit the reliability of model-based kinematic formulations, resulting in inaccurate Jacobian predictions, artificial singularities, and unstable actuation behavior. Motivated by these limitations, this work presents a complete model-less control framework that bypasses kinematic modeling by using an empirically initialized Jacobian refined online through differential convex updates. Tip motion is generated via a real-time quadratic program that computes actuator increments while enforcing tendon slack avoidance and geometric limits. A backbone-tension optimization term is introduced in this paper to regulate axial loading and suppress co-activation compression. The framework is validated across circular, pentagonal, and square trajectories, demonstrating smooth convergence, stable tension evolution, and sub-millimeter steady-state accuracy without any model calibration or parameter identification. These results establish the proposed controller as a scalable alternative to model-dependent continuum manipulation in a constrained environment.

Current upper limb prostheses aim to enhance user independence in daily activities by incorporating basic motor functions. However, they fall short of replicating the natural movement and interaction capabilities of the human arm. In contrast, human limbs leverage intrinsic compliance and actively modulate joint stiffness, enabling adaptive responses to varying tasks, impact absorption, and efficient energy transfer during dynamic actions. Inspired by this adaptability, we developed a transhumeral prosthesis with Variable Stiffness Actuators (VSAs) to replicate the controllable compliance found in biological joints. The proposed prosthesis features a modular design, allowing customization for different residual limb shapes and accommodating a range of independent control signals derived from users' biological cues. Integrated elastic elements passively support more natural movements, facilitate safe interactions with the environment, and adapt to diverse task requirements. This paper presents a comprehensive overview of the platform and its functionalities, highlighting its potential applications in the field of prosthetics.

Variable Stiffness Actuators prove invaluable for robotics applications in unstructured environments, fostering safe interactions and enhancing task adaptability. Nevertheless, their mechanical design inevitably results in larger and heavier structures compared to classical rigid actuators. This paper introduces a novel 3 Degrees of Freedom (DoFs) parallel wrist that achieves variable stiffness through redundant elastic actuation. Leveraging its parallel architecture, the device employs only four motors, rendering it compact and lightweight. This characteristic makes it particularly well-suited for applications in prosthetics or humanoid robotics. The manuscript delves into the theoretical model of the device and proposes a sophisticated control strategy for independent regulation of joint position and stiffness. Furthermore, it validates the proposed controller through simulation, utilizing a comprehensive analysis of the system dynamics. The reported results affirm the ability of the device to achieve high accuracy and disturbance rejection in rigid configurations while minimizing interaction forces with its compliant behavior.