基于松弛序列凸优化的轮式机器人协同轨迹规划

Coordination Trajectory Planning of Wheeled Robot Using Relaxation Sequential Convex Programming

针对威胁环境下的多智能体协同轨迹规划问题,以轮式机器人为对象,研究了基于序列凸优化方法的协同轨迹规划方法。首先通过对轮式机器人模型的分析,给出单独轮式机器人实际物理约束,同时以状态量、控制量加权为性能指标,考虑运动学方程、避障避碰约束、个体物理性能约束、终端约束,建立多轮式机器人协同轨迹规划问题;其次,对运动学方程、避障避碰约束进行凸化,证明了满足凸化后的避障避碰约束的解也满足原始避障避碰约束,并进行了几何直观解释;然后,将凸优化子问题进行离散化与松弛化,采用序列凸优化架构进行问题求解;最后,通过数值仿真,对比了松弛序列凸优化方法与现有非线性优化求解器的求解效率。结果表明,松弛序列凸优化方法在尽可能保证最优性的同时大大缩短了计算时间,具有一定工程意义。

Aiming at the problem of multi-agent coordination trajectory planning in threat environment,a method based on sequential convex optimization is proposed for wheeled robot.Firstly,through the analysis of the wheeled robot kinematic model,the actual input constraint of wheeled robot is given.The state variables and control variables are weighted as the cost.Secondly,a nonconvex cooperative trajectory planning problem of multi-wheeled robot is established,considering kinematics constraint,obstacle avoidance constraint,actual input constraint and terminal constraint.Thirdly,the noncovex problem is covexified,and it is proved that the solution which satisfies the convex constraint also satisfies the original constraint,and then the convex subproblem is discretized and relaxed,the sequential convex optimization framework is adopted to solve the problem.Finally,the efficiency of numerical simulation is compared with the existing nonlinear optimization solver.The results show that the relaxation sequential convex optimization method can ensure the optimality as much as possible and greatly shorten the calculation time,which has a certain engineering significance.