In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds on the tracking error. Such a controller is crucial in safe motion planning. We leverage the advanced theory in Control Contraction Metric and design a learning framework based on neural networks to co-synthesize the contraction metric and the controller for control-affine systems. We further provide methods to validate the convergence and bounded error guarantees. We demonstrate the performance of our method using a suite of challenging robotic models, including models with learned dynamics as neural networks. We compare our approach with leading methods using sum-of-squares programming, reinforcement learning, and model predictive control. Results show that our methods indeed can handle a broader class of systems with less tracking error and faster execution speed. Code is available at https://github.com/sundw2014/C3M.
We tackle the challenging problem of multi-agent cooperative motion planning for complex tasks described using signal temporal logic (STL), where robots can have nonlinear and nonholonomic dynamics. Existing methods in multi-agent motion planning, especially those based on discrete abstractions and model predictive control (MPC), suffer from limited scalability with respect to the complexity of the task, the size of the workspace, and the planning horizon. We present a method based on timed waypoints to address this issue. We show that timed waypoints can help abstract nonlinear behaviors of the system as safety envelopes around the reference path defined by those waypoints. Then the search for waypoints satisfying the STL specifications can be inductively encoded as a mixedinteger linear program. The agents following the synthesized timed waypoints have their tasks automatically allocated, and are guaranteed to satisfy the STL specifications while avoiding collisions. We evaluate the algorithm on a wide variety of benchmarks. Results show that it supports multi-agent planning from complex specification over long planning horizons, and significantly outperforms state-of-the-art abstraction-based and MPC-based motion planning methods. The implementation is available at https://github.com/sundw2014/STLPlanning.
Objectives To explore the difference between tracheostomy and non‐tracheostomy and identify the risk factors associated with the need for tracheostomy after traumatic cervical spinal cord injury (TCSCI). Methods The demographic and injury characteristics of 456 TCSCI patients, treated in the Xinqiao Hospital from 2010 to 2019, were retrospective analyzed. Patients were divided into the tracheostomy group (n = 63) and the non‐tracheostomy group (n = 393). Variables included were age, gender,smoking history, mechanism of injury, concomitant injury, American Spinal Injury Association (ASIA) Impairment Scale, the neurological level of injury, Cervical Spine Injury Severity Score (CSISS), surgery, and length of stay in ICU and hospital. SPSS 25.0 (SPSS, Chicago, IL) was used for statistical analysis and ROC curve drawing. Chi‐square analysis was applied to find out the difference of variables between the tracheostomy and non‐tracheostomy groups. Univariate logistic regression analysis (ULRA) and multiple logistic regression analysis (MLRA) were used to identify risk factors for tracheostomy. The area under the ROC curve (AUC) was used to evaluate the performance of these risk factors. Results Of 456 patients who met the inclusion criteria, 63 (13.8%) underwent tracheostomy. There were differences in age (χ2 = 6.615, P = 0.032), mechanism of injury (χ2 = 9.87, P = 0.036), concomitant injury (χ2 = 6.131, P = 0.013),ASIA Impairment Scale (χ2 = 123.08, P < 0.01), the neurological level of injury (χ2 = 34.74, P < 0.01), and CSISS (χ2 = 19.612, P < 0.01) between the tracheostomy and non‐tracheostomy groups. Smoking history, CSISS ≥ 7, AIS A and, NLI ≥ C5 were identified as potential risk factors for tracheostomy by ULRA. Smoking history (OR = 2.960, 95% CI: 1.524–5.750, P = 0.001), CSISS ≥ 7 (OR = 4.599, 95% CI: 2.328–9.085, P = 0.000), AIS A (OR = 14.213, 95% CI: 6.720–30.060, P = 0.000) and NLI ≥ C5 (OR = 8.312, 95% CI: 1.935–35.711, P = 0.004) as risk factors for tracheostomy were determined by MLRA. The AUC for the risk factors of tracheostomy after TCSCI was 0.858 (95% CI: 0.810–0.907). Conclusions Smoking history, CSISS ≥ 7, AIS A and, NLI ≥ C5 were identified as risk factors needing of tracheostomy in patients with TCSCI. These risk factors may be important to assist the clinical decision of tracheostomy.
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