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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) with formal safety guarantees 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 certifiable semidefinite constraints can be enforced at real-time rates for agile embedded robotics. 

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 could select and account for social objectives related to navigation autonomously.