基于凸优化的举高消防车时间最优轨迹规划
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摘要
为提高举高消防车作业的及时性、可靠性与安全性,提出一种考虑动作平稳、无冲击的时间最优轨迹规划算法。引入伪位移参量s表示路径,利用B样条曲线对举高消防车臂架系统各个关节运动离散点进行拟合,构造连续运动几何路径。结合连续路径,以s及其对于时间的各阶导数表示时间最优目标函数与各个关节速度、加速度约束,建立时间最优轨迹规划的凸优化模型。利用B样条曲线以有限维矢量x表示轨迹,采用内点法对凸优化模型进行求解,在保证速度、加速度、加加速度连续的条件下求得最优解,进而得到各个关节的运动轨迹。利用提出的方法对大高度举高消防车进行轨迹规划,经仿真表明,在满足动作平稳性的同时得到时间最优运动轨迹。
In order to improve the timeliness, reliability and security of elevating fire truck, a time optimal trajectory planning algorithm is proposed, considering the stability and non-impact of motions. Pseudo-displacement s is introduced, to fit discrete points of joints motion and construct continuous geometric path with B-spline. A convex optimization model is established, which is based on the continuous path, time optimal objective function that is formulated with s and its derivatives of time, as well as joint velocity and acceleration constraints. B-spline is utilized to parameterize trajectories with finite-dimensional vector x, and interior point method is used to solvethe convex optimization model, to get optimal trajectories of joints, while guaranteeing that velocities,accelerations and jerks are continuous. The proposed algorithm is simulated on a high elevating fire truck, and the results demonstrate that time optimal trajectory is obtained while the stability of motion is satisfied.
In order to improve the timeliness, reliability and security of elevating fire truck, a time optimal trajectory planning algorithm is proposed, considering the stability and non-impact of motions. Pseudo-displacement s is introduced, to fit discrete points of joints motion and construct continuous geometric path with B-spline. A convex optimization model is established, which is based on the continuous path, time optimal objective function that is formulated with s and its derivatives of time, as well as joint velocity and acceleration constraints. B-spline is utilized to parameterize trajectories with finite-dimensional vector x, and interior point method is used to solvethe convex optimization model, to get optimal trajectories of joints, while guaranteeing that velocities,accelerations and jerks are continuous. The proposed algorithm is simulated on a high elevating fire truck, and the results demonstrate that time optimal trajectory is obtained while the stability of motion is satisfied.
引文
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[13]王欣,高凌翀,黄兆秋,等.直臂高空作业车船体喷涂轨迹控制研究与仿真[J].系统仿真学报,2016,28(2):404-409.WANG Xin,GAO Lingchong,HUANG Zhaoqiu,et al.Research and simulation on trajectory control of telescopic boom aerial work platform for hull spray painting[J].Journal of System Simulation,2016,28(2):404-409.
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[2]钱东海,谭伟,赵锡芳.基于B样条路径的机器人时间最优轨迹规划[J].上海交通大学学报,1998,32(12):31-35.QIAN Donghai,TAN Wei,ZHAO Xifang.Time optimum trajectory planning for robots based on B-spline path[J].Journal of Shanghai Jiao Tong University,1998,32(12):31-35.
[3]CHO B H,CHOI B S,LEE J M.Time-optimal trajectory planning for a robot system under torque and impulse constraints[J].International Journal of Control Automation&Systems,2006,4(1):10-16.
[4]BIANCO C,PIAZZI A.Minimum-time trajectory planning of mechanical manipulators under dynamic constraints[J].International Journal of Control,2002,75(13):967-980.
[5]KHOUKHI A,BARON L,BALAZINSKI M,et al.Ahierarchical neuro-fuzzy system to near optimal-time trajectory planning of redundant manipulators[J].Engineering Applications of Artificial Intelligence,2008,21(7):974-984.
[6]GAO M,DING P,YANG Y.Time-optimal trajectory planning of industrial robots based on particle swarm optimization[C]//International Conference on Instrumentation&Measurement.Piscataway:IEEE,2015:1934-1939.
[7]SURYAWAN F,DONáJ,SERON M.Minimum-time trajectory generation for constrained linear systems using flatness and B-splines[J].International Journal of Control,2011:1565-1585.
[8]KAMALAPURKAR R,DINH H,BHASIN S,et al.Approximate optimal trajectory tracking for continuous-time nonlinear systems[J].Automatica,2015,51:40-48.
[9]LIU H,LAI X,WU W.Time-optimal and jerk-continuous trajectory planning for robot manipulators with kinematic constraints[J].Robotics and Computer-integrated Manufacturing,2013,29(2):309-317.
[10]REYNOSO-MORA P,CHEN W,TOMIZUKA M.On the time-optimal trajectory planning and control of robotic manipulators along predefined paths[C]//American Control Conference.Piscataway:IEEE,2013:371-377.
[11]滕儒民.高空作业车臂架系统快速设计及其运动规划研究[D].大连:大连理工大学,2012.TENG Rumin.Rapid design and motion planning of the boom system for the aerial work platform[D].Dalian:Dalian University of Technology,2012.
[12]袁合.折臂式高空作业车轨迹规划与控制研究[D].大连:大连理工大学,2013.YUAN He.Track programming and controlling of folding boom aerial working platform[D].Dalian:Dalian University of Technology,2013.
[13]王欣,高凌翀,黄兆秋,等.直臂高空作业车船体喷涂轨迹控制研究与仿真[J].系统仿真学报,2016,28(2):404-409.WANG Xin,GAO Lingchong,HUANG Zhaoqiu,et al.Research and simulation on trajectory control of telescopic boom aerial work platform for hull spray painting[J].Journal of System Simulation,2016,28(2):404-409.
[14]滕儒民,贺浩,项慧,等.基于启发式路径搜索的高空作业车避障轨迹规划[J].机械工程学报,2013,49(10):194-198.TENG Rumin,HE Hao,XIANG Hui,et al.Trajectory planning with obstacles considered for aerial work platform based on heuristic path-searching[J].Journal of Mechanical Engineering,2013,49(10):194-198.
[15]VERSCHEURE D,DEMEULENAERE B,SWEVERS J,et al.Time-optimal path tracking for robots:A convex optimization approach[J].IEEE Transactions on Automatic Control,2009,54(10):2318-2327.
[16]REITER A.Time-optimal trajectory planning for redundant robots[M].Wiesbaden:Springer Verlag,2016.