Abstract:
This work proposes a safety-critical local reactive controller that enables the robot to navigate in unknown and cluttered environments. In particular, the trajectory tracking task is formulated as a constrained polynomial optimization problem. Then, safety constraints are imposed on the control variables invoking the notion of polynomial positivity certificates in conjunction with their Sum-of-Squares (SOS) approximation, thereby confining the robot motion inside the locally extracted convex free region. It is noteworthy that, in the process of devising the proposed safety constraints, the geometry of the robot can be approximated using any shape that can be characterized with a set of polynomial functions. The optimization problem is further convexified into a semidefinite program (SDP) leveraging truncated multi-sequences (tms) and moment relaxation, which favorably facilitates the effective use of off-the-shelf conic programming solvers, such that real-time performance is attainable. Various robot navigation tasks are investigated to demonstrate the effectiveness of the proposed approach in terms of safety and tracking performance.

Abstract:
Cooperative trajectory planning of connected autonomous vehicles (CAVs) generally admits strong nonlinearity and non-convexity, rendering great difficulties in finding the optimal solution. Existing methods typically suffer from low computational efficiency and poor scalability, which hinder the appropriate applications in large-scale scenarios involving an increasing number of vehicles. To tackle this problem, we propose a novel decentralized iterative linear quadratic regulator (iLQR) algorithm by leveraging the dual consensus alternating direction method of multipliers (ADMM). First, the original non-convex optimization problem is reformulated into a series of convex optimization problems through iterative neighbourhood approximation. Then, the dual of each convex optimization problem is shown to have a consensus structure, which facilitates the use of consensus ADMM to solve for the dual solution in a fully decentralized and parallel architecture. Finally, the primal solution corresponding to the trajectory of each vehicle is recovered by solving a linear quadratic regulator (LQR) problem iteratively, and a novel trajectory update strategy is proposed to ensure the dynamic feasibility of vehicles. With the proposed development, the computation burden is significantly alleviated such that real-time performance is attainable. Two traffic scenarios are presented to validate the proposed algorithm, and thorough comparisons between our proposed method and baseline methods (including centralized iLQR, IPOPT, and SQP) are conducted to demonstrate the scalability of the proposed approach.