Varun Madabushi

Xiaoyu Zhang, Steven Haener, Varun Madabushi et al.

We present the KinoDynamic Motion Retargeting (KDMR) framework, a novel approach for humanoid locomotion that models the retargeting process as a multi-contact, whole-body trajectory optimization problem. Conventional kinematics-based retargeting methods rely solely on spatial motion capture (MoCap) data, inevitably introducing physically inconsistent artifacts, such as foot sliding and ground penetration, that severely degrade the performance of downstream imitation learning policies. To bridge this gap, KDMR extends beyond pure kinematics by explicitly enforcing rigid-body dynamics and contact complementarity constraints. Further, by integrating ground reaction force (GRF) measurements alongside MoCap data, our method automatically detects heel-toe contact events to accurately replicate complex human-like contact patterns. We evaluate KDMR against the state-of-the-art baseline, GMR, across three key dimensions: 1) the dynamic feasibility and smoothness of the retargeted motions, 2) the accuracy of GRF tracking compared to raw source data, and 3) the training efficiency and final performance of downstream control policies trained via the BeyondMimic framework. Experimental results demonstrate that KDMR significantly outperforms purely kinematic methods, yielding dynamically viable reference trajectories that accelerate policy convergence and enhance overall locomotion stability. Our end-to-end pipeline will be open-sourced upon publication.

Varun Madabushi, Elizabeth Dietrich, Hanna Krasowski et al.

Poincare return maps are a fundamental tool for analyzing periodic orbits in hybrid dynamical systems, including legged locomotion, power electronics, and other cyber-physical systems with switching behavior. The Poincare return map captures the evolution of the hybrid system on a guard surface, reducing the stability analysis of a periodic orbit to that of a discrete-time system. While linearization provides local stability information, assessing robustness to disturbances requires identifying invariant sets of the state space under the return dynamics. However, computing such invariant sets is computationally difficult, especially when system dynamics are only available through forward simulation. In this work, we propose an algorithmic framework leveraging sampling-based optimization to compute a finite-step invariant ellipsoid around a nominal periodic orbit using sampled evaluations of the return map. The resulting solution is accompanied by probabilistic guarantees on finite-step invariance satisfying a user-defined accuracy threshold. We demonstrate the approach on two low-dimensional systems and a compass-gait walking model.

Varun Madabushi, Akash Harapanahalli, Samuel Coogan et al.

For hybrid systems exhibiting periodic behavior, analyzing the invariant set containing the limit cycle is a natural way to study the robustness of the closed-loop system. However, computing these sets can be computationally expensive, especially when applied to contact-rich cyber-physical systems such as legged robots. In this work, we extend existing methods for overapproximating reachable sets of continuous systems using parametric embeddings to compute a forward-invariant set around the nominal trajectory of a simplified model of a bipedal robot. Our three-step approach (i) computes an overapproximating reachable set around the nominal continuous flow, (ii) catalogs intersections with the guard surface, and (iii) passes these intersections through the reset map. If the overapproximated reachable set after one step is a strict subset of the initial set, we formally verify a forward invariant set for this hybrid periodic orbit. We verify this condition on the bipedal walker model numerically using immrax, a JAX-based library for parametric reachable set computation, and use it within a bi-level optimization framework to design a tracking controller that maximizes the size of the invariant set.