False Feasibility in Variable Impedance MPC for Legged Locomotion

Variable impedance model predictive control (MPC) formulations that treat joint stiffness as an instantaneous decision variable operate on a feasible set strictly larger than the physically realizable set under first-order actuator dynamics. We identify this as a formulation error rather than a modeling approximation, formalize the distinction between the parameter-based feasible set Fparam and the realizable set Freal, and characterize the regime of mismatch via the dimensionless parameter alpha = omega_sT (actuator bandwidth times task timescale). For the 1D hopping monoped, we prove that below an analytical threshold alpha_crit derived in closed form from task physics, no admissible stiffness command realizes the parameter-based prediction. Numerical validation in 1D shows monotonic deviation growth as alpha decreases, with the predicted scaling holding across ten parameter combinations (log-log R2 = 0.99). Mechanism transfer to planar spring-loaded inverted pendulum dynamics confirms center-of-mass and stance-timing deviation as the primary consequence, with regime-dependent friction effects as a tertiary observable. A second threshold alpha_infeas < alpha_crit establishes a floor below which restricting the admissible stiffness range cannot repair realizability, closing the conservative-tuning objection on structural grounds. Augmenting the prediction state with stiffness closes the mismatch by construction.

Decentralised, Scalable and Privacy-Preserving Synthetic Data Generation

Synthetic data is emerging as a promising way to harness the value of data, while reducing privacy risks. The potential of synthetic data is not limited to privacy-friendly data release, but also includes complementing real data in use-cases such as training machine learning algorithms that are more fair and robust to distribution shifts etc. There is a lot of interest in algorithmic advances in synthetic data generation for providing better privacy and statistical guarantees and for its better utilisation in machine learning pipelines. However, for responsible and trustworthy synthetic data generation, it is not sufficient to focus only on these algorithmic aspects and instead, a holistic view of the synthetic data generation pipeline must be considered. We build a novel system that allows the contributors of real data to autonomously participate in differentially private synthetic data generation without relying on a trusted centre. Our modular, general and scalable solution is based on three building blocks namely: Solid (Social Linked Data), MPC (Secure Multi-Party Computation) and Trusted Execution Environments (TEEs). Solid is a specification that lets people store their data securely in decentralised data stores called Pods and control access to their data. MPC refers to the set of cryptographic methods for different parties to jointly compute a function over their inputs while keeping those inputs private. TEEs such as Intel SGX rely on hardware based features for confidentiality and integrity of code and data. We show how these three technologies can be effectively used to address various challenges in responsible and trustworthy synthetic data generation by ensuring: 1) contributor autonomy, 2) decentralisation, 3) privacy and 4) scalability. We support our claims with rigorous empirical results on simulated and real datasets and different synthetic data generation algorithms.