高技术通讯
高技術通訊
고기술통신
HIGH TECHNOLOGY LETTERS
2014年
10期
85-96
,共12页
赵建军%魏毅%朱登明%夏时洪%王兆其
趙建軍%魏毅%硃登明%夏時洪%王兆其
조건군%위의%주등명%하시홍%왕조기
轨迹规划%时间约束%凸规划%二阶锥规划(SOCP)
軌跡規劃%時間約束%凸規劃%二階錐規劃(SOCP)
궤적규화%시간약속%철규화%이계추규화(SOCP)
path tracking%time constraints%convex optimization%second order cone programming
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。
研究瞭快速求解具有時間約束的機械臂軌跡規劃問題，提齣瞭一種基于凸規劃的軌跡規劃方法。該方法針對機械臂軌跡規劃中動力學約束非線性彊、時間約束不易處理的問題，首先通過變量替換，將非線性約束轉化為線性約束，然後添加新的約束，將原始非凸優化問題轉化為凸規劃問題，在此基礎上，將其寫作二階錐規劃（SOCP）形式，使用SeDuMi等優化工具包近似實時求解。該方法具有以下優點：計算高效，凸規劃問題能夠在多項式時間內得到求解；算法全跼穩定，能收斂到全跼最優解，不需要提供優化初值；可擴展性彊，工業機器人的多種約束以及性能指標如加速度平滑約束、功率等均可擴充。倣真實驗錶明，與現有方法相比，該方法能夠有效提高軌跡規劃的效率，機器人的軌跡規劃可以近似實時求解。
연구료쾌속구해구유시간약속적궤계비궤적규화문제，제출료일충기우철규화적궤적규화방법。해방법침대궤계비궤적규화중동역학약속비선성강、시간약속불역처리적문제，수선통과변량체환，장비선성약속전화위선성약속，연후첨가신적약속，장원시비철우화문제전화위철규화문제，재차기출상，장기사작이계추규화（SOCP）형식，사용SeDuMi등우화공구포근사실시구해。해방법구유이하우점：계산고효，철규화문제능구재다항식시간내득도구해；산법전국은정，능수렴도전국최우해，불수요제공우화초치；가확전성강，공업궤기인적다충약속이급성능지표여가속도평활약속、공솔등균가확충。방진실험표명，여현유방법상비，해방법능구유효제고궤적규화적효솔，궤기인적궤적규화가이근사실시구해。
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.
