基于凸规划的机械臂轨迹规划方法

摘要

The problem of fast solving a robot manipulator’s path tracking with time constraints was studied, and a novel path tracking approach based on convex optimization was presented. To overcome the difficulties in dealing with the strong nonlinear dynamic constraints and time constraints in path tracking, the presented approach converts the nonlinear constraints into linear constraints by replacement of variables, and then adds new constraints to convert the original non convex optimization problem into a convex optimization problem, furthermore, converts it into a second order cone program (SOCP), and uses the optimization tools such as the SeDuMi to conduct the real time solving. This approach has several advantages. Firstly, SOCP problems can be solved in polynomial time by the interior point methods. Secondly, the convex optimization is globally stable and the solution is globally optimal. Besides, there is no need to provide initial values for the optimization. Thirdly, this approach has great flexibility and can be applied to the more complicated circumstances where some other types of constraints and objective functions can be taken into account, such as acceleration constraints, minimum energy objective function and minimum jerk objective function. The simulations on a six degrees of freedom robot manipulator show the better efficiency and effectiveness of the proposed approach.%研究了快速求解具有时间约束的机械臂轨迹规划问题，提出了一种基于凸规划的轨迹规划方法。该方法针对机械臂轨迹规划中动力学约束非线性强、时间约束不易处理的问题，首先通过变量替换，将非线性约束转化为线性约束，然后添加新的约束，将原始非凸优化问题转化为凸规划问题，在此基础上，将其写作二阶锥规划（SOCP）形式，使用SeDuMi等优化工具包近似实时求解。该方法具有以下优点：计算高效，凸规划问题能够在多项式时间内得到求解；算法全局稳定，能收敛到全局最优解，不需要提供优化初值；可扩展性强，工业机器人的多种约束以及性能指标如加速度平滑约束、功率等均可扩充。仿真实验表明，与现有方法相比，该方法能够有效提高轨迹规划的效率，机器人的轨迹规划可以近似实时求解。