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Abstract Quadrotors can provide services such as infrastructure inspection and search-and-rescue, which require operating autonomously in cluttered environments. Autonomy is typically achieved with receding-horizon planning, where a short plan is executed while a new one is computed, because sensors receive limited information at any time. To ensure safety and prevent robot loss, plans must be verified as collision free despite uncertainty (e.g, tracking error). Existing spline-based planners dilate obstacles uniformly to compensate for uncertainty, which can be conservative. On the other hand, reachability-based planners can include trajectory-dependent uncertainty as a function of the planned trajectory. This work applies Reachability-based Trajectory Design (RTD) to plan quadrotor trajectories that are safe despite trajectory-dependent tracking error. This is achieved by using zonotopes in a novel way for online planning. Simulations show aggressive flight up to 5 m/s with zero crashes in 500 cluttered, randomized environments. 

Falls affect a growing number of the population each year. Clinical methods to assess fall risk usually evaluate the performance of specific motions such as balancing or Sit-to-Stand. Unfortunately, these techniques have been shown to have poor predictive power, and are unable to identify the portions of motion that are most unstable. To this end, it may be useful to identify the set of body configurations that can accomplish a task under a specified control strategy. The resulting strategy-specific boundary between stable and unstable motion could be used to identify individuals at risk of falling. The recently proposed Stability Basin is defined as the set of configurations through time that do not lead to failure for an individual under their chosen control strategy. This paper presents a novel method to compute the Stability Basin and the first experimental validation of the Stability Basin with a perturbative Sit-to-Stand experiment involving forwards or backwards pulls from a motor-driven cable with 11 subjects. The individually-constructed Stability Basins are used to identify when a trial fails, i.e. when an individual must switch from their chosen control strategy (indicated by a step or sit) to recover from a perturbation. The constructed Stability Basins correctly predict the outcome of trials where failure was observed with over 90 % accuracy, and correctly predict the outcome of successful trials with over 95 % accuracy. The Stability Basin was compared to three other methods and was found to estimate the stable region with over 45 % more accuracy in all cases. This study demonstrates that Stability Basins offer a novel model-based approach for quantifying stability during motion, which could be used in physical therapy for individuals at risk of falling.