Fausto Vega

Ishaan Mahajan, Jon Arrizabalaga, Andrea Grillo et al.

Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on resource-constrained embedded systems. To address this gap, we introduce TinySDP, the first semidefinite programming solver designed for embedded systems, enabling real-time model-predictive control (MPC) on microcontrollers for problems with nonconvex obstacle constraints. Our approach integrates positive-semidefinite cone projections into a cached-Riccati-based ADMM solver, leveraging computational structure for embedded tractability. We pair this solver with an a posteriori rank-1 certificate that converts relaxed solutions into explicit geometric guarantees at each timestep. On challenging benchmarks, e.g., cul-de-sac and dynamic obstacle avoidance scenarios that induce failures in local methods, TinySDP achieves collision-free navigation with up to 73% shorter paths than state-of-the-art baselines. We validate our approach on a Crazyflie quadrotor, demonstrating that semidefinite constraints can be enforced at real-time rates for agile embedded robotics.

Santosh Balajee Banisetty, Vineeth Rajamohan, Fausto Vega et al.

We present a context classification pipeline to allow a robot to change its navigation strategy based on the observed social scenario. Socially-Aware Navigation considers social behavior in order to improve navigation around people. Most of the existing research uses different techniques to incorporate social norms into robot path planning for a single context. Methods that work for hallway behavior might not work for approaching people, and so on. We developed a high-level decision-making subsystem, a model-based context classifier, and a multi-objective optimization-based local planner to achieve socially-aware trajectories for autonomously sensed contexts. Using a context classification system, the robot can select social objectives that are later used by Pareto Concavity Elimination Transformation (PaCcET) based local planner to generate safe, comfortable, and socially-appropriate trajectories for its environment. This was tested and validated in multiple environments on a Pioneer mobile robot platform; results show that the robot was able to select and account for social objectives related to navigation autonomously.