Optimal Energy Consumption Trajectory Planning for Mobile Robot Based on Motion Control and Frequency Domain Analysis
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摘要: 本文针对两轮自平衡可移动机器人, 提出了一种新的能耗最优运动轨迹规划方法.本文将轨迹规划与由轨迹跟踪控制器和机器人动力学方程组成的运动控制模型相结合, 基于期望轨迹与实际电机输入电压间的传递函数和能量在时域和频域上的对应关系, 通过频域分析的方法得到了具有明确机理表达的线性能耗模型, 并采用最小二乘线性回归法对模型参数进行辨识.对于能耗最优轨迹, 由全局路径规划得到的路径点作为局部轨迹规划的局部目标点, 通过一定的数学转换和参数求导, 可直接得到相邻两个局部目标点间的能耗最优运行轨迹和对应的运行时间.通过仿真实验证明了本文所提能耗模型的准确性和所得轨迹的能耗最优性.Abstract: In this paper, a new optimal trajectory planning algorithm to minimize energy consumption for two-wheeled self-balancing motion robot is proposed. The trajectory planning is combined with the motion control model composed of trajectory tracking controller and robot dynamics model, and based on the transfer function between the desired trajectory and actual motor input voltage and the corresponding relationship of energy in time domain and frequency domain, a linear energy consumption model with clear mechanism expression is obtained by frequency-domain analysis and the model parameters are identified by the least square linear regression method. For the optimal trajectory, select the way points obtained by global path planning as the local target points of the local trajectory planning, through a certain mathematical transformations and derivative of parameters, the optimal operational trajectory and operational time of each two target points are determined directly. Through simulation experiments, the accuracy of the proposed energy consumption model and minimum energy consumption of the obtained trajectory are verified.
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Key words:
- Trajectory planning /
- minimum energy consumption /
- motion robot /
- frequency-domain analysis
1) 本文责任编委 贺威 -
图 1 机器人实际路径与期望路径对比图以及对应的控制器动态过程示意图
Fig. 1 The actual path of the robot is compared with the expected path and the controller dynamic process
图 2 两轮自平衡小车侧视图与俯视图
Fig. 2 The side view and top view of two-wheel self-balancing robot
图 3 本文采用的轨迹规划和控制系统体系结构
Fig. 3 Architecture of the mobile robot trajectory planning and control system in this paper
图 5 能耗模型验证集拟合效果误差图
Fig. 5 Modeling errors of energy consumption model in validation set
图 7 能耗最优期望轨迹与实际轨迹对比图
Fig. 7 Comparison diagram of the optimal energy consumption desired trajectory and actual trajectory
图 8 能耗最优期望轨迹与实际轨迹坐标误差图
Fig. 8 Coordinate error graph of the optimal energy consumption desired trajectory and actual trajectory
图 9 真实能耗与运行时间和轨迹圆心角关系图
Fig. 9 The relational graph of real energy consumption with running time and track circle angle
表 1 两轮自平衡机器人模型参数
Table 1 Two-wheel self-balancing robot model parameters
机器人参数 参数值 $M$ 机器人质量 3.2 (kg) $R$ 车轮半径 0.15 (m) $W$ 车体宽度 0.35 (m) $f_m$ 电机与轮轴摩擦系数 0.0022 $f_w$ 车轮与地面摩擦系数 0.035 $R_m$ 电机内阻 6.69 ($\Omega$) $P_s$ 非机械元件功率 6 (w) 
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表 2 两轮自平衡机器人初始能耗模型参数
Table 2 Initial energy consumption model parameters of two-wheel self-balancing robot
参数 数值 参数 数值 参数 数值 $a1$ 172.2 $a6$ 1.37 $a11$ 4.27 $a2$ 7.57 $a7$ 16.26 $a12$ 1.09 $a3$ 13.2 $a8$ $-$4.39 $a13$ 5.82 $a4$ $-$0.66 $a9$ $-$1.11 $b1$ 20.83 $a5$ $-$0.94 $a10$ 15.97 $b2$ 0.93
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表 3 能耗最优轨迹仿真结果
Table 3 Energy consumption optimal trajectory simulation results
轨迹序列 分段能耗$E_{\rm {total}}$ (J) 运行时间$T$(s) 线速度$v$ (m/s) 角速度$w $(rad/s) 方向角改变$\sigma$ (°) 1 336.97 28.46 0.499 0.011 36.28 2 252.43 21.42 0.523 $-$0.011 $-$20.68 3 256.15 21.38 0.526 0.017 33.06 4 270.15 21.62 0.527 0.03 61
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表 4 与其他方法仿真结果比较
Table 4 Compare with other methods simulation results
轨迹序列 能耗最优算法 路径最短策略 三次贝塞尔曲线 1 336.97 338.15 345.5 2 252.43 252.03 265.72 3 256.15 255.89 290.72 4 270.15 283.82 292.3 总能耗(J) 1 115.7 1 129.8 1 203.3 运行时间(s) 92.88 92.88 81.32 能耗比率(%) 100 101.26 107.85
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表 5 与其他方法仿真结果比较
Table 5 Compare with other methods simulation results
轨迹序列 能耗最优算法 路径最短策略 三次贝塞尔曲线 1 28.43 30.811 26.03 2 40.56 39.87 52.4 3 33.61 36.36 35.12 4 33.89 33.62 36.12 5 30.91 30.93 32.33 6 28.57 29.02 28.82 7 24.68 24.56 25.28 总能耗(J) 220.64 225.18 236.1 运行时间(s) 18.6 18.6 15.3 能耗比率(%) 100 102.06 107
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