Robust Tracking with Model Mismatch for Fast and Safe Planning: an SOS Optimization Approach
Robust Tracking with Model Mismatch for Fast and Safe Planning: an SOS Optimization Approach
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模型不匹配的鲁棒跟踪可实现快速安全的规划：SOS 优化方法
DOI：
10.1007/978-3-030-44051-0_32
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
M. Pavone
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文献类型：
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作者：
Sumeet Singh;Mo Chen;Sylvia L. Herbert;C. Tomlin;M. Pavone
在追求实时运动规划时，一种普遍采用的做法是通过在一个简化的低维动态模型上运行规划算法来计算轨迹，然后采用一个反馈跟踪控制器，该控制器通过考虑完整的高维系统动态来跟踪这样的轨迹。虽然这种存在模型不匹配的规划策略通常能产生较快的计算时间，但无法保证动态可行性，这阻碍了其在安全关键系统中的应用。基于近期通过哈密顿 - 雅可比（HJ）可达性视角解决这一问题的工作，我们设计了一个算法框架，通过该框架，对于一对“规划器”（即低维）和“跟踪器”（即高维）模型，可以离线计算一个反馈跟踪控制器以及相关的跟踪界限。然后在通过低维模型生成运动规划时，将此界限用作安全余量。具体而言，我们利用平方和（SOS）编程的计算工具来设计一个双线性优化算法，用于计算反馈跟踪控制器和相关的跟踪界限。通过数值实验对该算法进行了演示，重点研究了SOS所提供的计算可扩展性的提高与其内在保守性之间的权衡。总体而言，我们的结果使得在保持安全保证的同时，能够将具有模型不匹配的有吸引力的规划策略扩展到HJ分析无法触及的系统。
In the pursuit of real-time motion planning, a commonly adopted practice is to compute a trajectory by running a planning algorithm on a simplified, low-dimensional dynamical model, and then employ a feedback tracking controller that tracks such a trajectory by accounting for the full, high-dimensional system dynamics. While this strategy of planning with model mismatch generally yields fast computation times, there are no guarantees of dynamic feasibility, which hampers application to safety-critical systems. Building upon recent work that addressed this problem through the lens of Hamilton-Jacobi (HJ) reachability, we devise an algorithmic framework whereby one computes, offline, for a pair of "planner" (i.e., low-dimensional) and "tracking" (i.e., high-dimensional) models, a feedback tracking controller, and associated tracking bound. This bound is then used as a safety margin when generating motion plans via the low-dimensional model. Specifically, we harness the computational tool of sum-of-squares (SOS) programming to design a bilinear optimization algorithm for the computation of the feedback tracking controller and associated tracking bound. The algorithm is demonstrated via numerical experiments, with an emphasis on investigating the trade-off between the increased computational scalability afforded by SOS and its intrinsic conservativeness. Collectively, our results enable scaling the appealing strategy of planning with model mismatch to systems that are beyond the reach of HJ analysis, while maintaining safety guarantees.