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A key challenge to ensuring the rapid transition of robotic systems from the industrial sector to more ubiquitous applications is the development of algorithms that can guarantee safe operation while in close proximity to humans. Motion planning and control methods, for instance, must be able to certify safety while operating in real-time in arbitrary environments and in the presence of model uncertainty. This paper proposes Wrench Analysis for Inertial Transport using Reachability (WAITR), a certifiably safe motion planning and control framework for serial link manipulators that manipulate unsecured objects in arbitrary environments. WAITR uses reachability analysis to construct over-approximations of the contact wrench applied to unsecured objects, which captures uncertainty in the manipulator dynamics, the object dynamics, and contact parameters such as the coefficient of friction. An optimization problem formulation is presented that can be solved in real-time to generate provably-safe motions for manipulating the unsecured objects. This paper illustrates that WAITR outperforms state of the art methods in a variety of simulation experiments and demonstrates its performance in the real-world., Comment: 8 pages, 3 figures. For project page with code, videos, and supplementary appendices, see https://roahmlab.github.io/waitr-dev/. arXiv admin note: text overlap with arXiv:2301.13308

Ensuring safe, real-time motion planning in arbitrary environments requires a robotic manipulator to avoid collisions, obey joint limits, and account for uncertainties in the mass and inertia of objects and the robot itself. This paper proposes Autonomous Robust Manipulation via Optimization with Uncertainty-aware Reachability (ARMOUR), a provably-safe, receding-horizon trajectory planner and tracking controller framework for robotic manipulators to address these challenges. ARMOUR first constructs a robust controller that tracks desired trajectories with bounded error despite uncertain dynamics. ARMOUR then uses a novel recursive Newton-Euler method to compute all inputs required to track any trajectory within a continuum of desired trajectories. Finally, ARMOUR over-approximates the swept volume of the manipulator; this enables one to formulate an optimization problem that can be solved in real-time to synthesize provably-safe motions. This paper compares ARMOUR to state of the art methods on a set of challenging manipulation examples in simulation and demonstrates its ability to ensure safety on real hardware in the presence of model uncertainty without sacrificing performance. Project page: https://roahmlab.github.io/armour/., Comment: 20 pages, 6 figures

People with lower-limb loss, the majority of which use passive prostheses, exhibit a high incidence of falls each year. Powered lower-limb prostheses have the potential to reduce fall rates by actively helping the user recover from a stumble, but the unpredictability of the human response makes it difficult to design controllers that ensure a successful recovery. This paper presents a method called TRIP-RTD (Trip Recovery in Prostheses via Reachability-based Trajectory Design) for online trajectory planning in a knee prosthesis during and after a stumble that can accommodate a set of possible predictions of human behavior. Using this predicted set of human behavior, the proposed method computes a parameterized reachable set of trajectories for the human-prosthesis system. To ensure safety at run-time, TRIP-RTD selects a trajectory for the prosthesis that guarantees that all possible states of the human-prosthesis system at touchdown arrive in the basin of attraction of the nominal behavior of the system. In simulated stumble experiments where a nominal phase-based controller was unable to help the system recover, TRIP-RTD produced trajectories in under 101 ms that led to successful recoveries for all feasible solutions found., Comment: 8 pages, 3 figures

For robotic arms to operate in arbitrary environments, especially near people, it is critical to certify the safety of their motion planning algorithms. However, there is often a trade-off between safety and real-time performance; one can either carefully design safe plans, or rapidly generate potentially-unsafe plans. This work presents a receding-horizon, real-time trajectory planner with safety guarantees, called ARMTD (Autonomous Reachability-based Manipulator Trajectory Design). The method first computes (offline) a reachable set of parameterized trajectories for each joint of an arm. Each trajectory includes a fail-safe maneuver (braking to a stop). At runtime, in each receding-horizon planning iteration, ARMTD constructs a parameterized reachable set of the full arm in workspace and intersects it with obstacles to generate sub-differentiable, provably-conservative collision-avoidance constraints on the trajectory parameters. ARMTD then performs trajectory optimization over the parameters, subject to these constraints. On a 6 degree-of-freedom arm, ARMTD outperforms CHOMP in simulation, never crashes, and completes a variety of real-time planning tasks on hardware., Comment: 14 pages, 4 figures

Falls affect a growing number of the population each year. Clinical methods to identify those at greatest risk for falls usually evaluate individuals while they perform specific motions such as balancing or Sit-to-Stand (STS). Unfortunately these techniques have been shown to have poor predictive power and are unable to identify the magnitude, direction, and timing of perturbations that can cause an individual to lose stability during motion. To address this limitation, the recently proposed Stability Basin (SB) aims to characterize the set of perturbations that will cause an individual to fall under a specific motor control strategy. The SB is defined as the set of configurations that do not lead to failure for an individual under their chosen control strategy. This paper presents a novel method to compute the SB and the first experimental validation of the SB with an 11-person perturbative STS experiment involving forwards or backwards pulls from a motor-driven cable. The individually-constructed SBs are used to identify when a trial fails, i.e., when an individual must switch control strategies (indicated by a step or sit) to recover from a perturbation. The constructed SBs 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 SB 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 SBs offer a novel model-based approach for quantifying stability during motion, which could be used in physical therapy for individuals at risk of falling., Comment: 19 pages, 9 figures

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., Comment: 12 Pages, 3 Figures, 1 Table

Anterior cruciate ligament (ACL) reconstruction necessitates months of rehabilitation, during which a clinician evaluates whether a patient is ready to return to sports or occupation. Due to their time- and cost-intensive nature, these screenings to assess progress are unavailable to many. This paper introduces an automated, markerless, camera-based method for estimating rehabilitation criteria following ACL reconstruction. To evaluate the performance of this novel technique, data were collected weekly from 12 subjects as they used a leg press over the course of a 12-week rehabilitation period. The proposed camera-based method for estimating displacement and force was compared to encoder and force plate measurements. The leg press displacement and force values were estimated with 89.7% and 85.3% accuracy, respectively. These values were then used to calculate lower-limb symmetry and to track patient progress over time., Comment: 6 pages

Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the interactions with the environment; however, one must still guarantee that the model, despite uncertainty, behaves acceptably. This paper presents a convex optimization method to efficiently compute the set of configurations of a polynomial dynamical system that are able to safely reach a user defined target set despite parametric uncertainty in the model. Since planning in the presence of uncertainty can lead to undesirable conservatives, this paper computes those trajectories of the uncertain nonlinear systems which are $\alpha$-probable of reaching the desired configuration. The presented approach uses the notion of occupation measures to describe the evolution of trajectories of a nonlinear system with parametric uncertainty as a linear equation over measures whose supports coincide with the trajectories under investigation. This linear equation is approximated with vanishing conservatism using a hierarchy of semidefinite programs each of which is proven to compute an approximation to the set of initial conditions that are $\alpha$-probable of reaching the user defined target set safely in spite of uncertainty. The efficacy of this method is illustrated on four systems with parametric uncertainty., Comment: 7 pages, 4 figures