脚掌转动的跳跃机器人轨迹规划与落地稳定性分析
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摘要
近几十年来，腿型机器人一直成为移动机器人领域中的研究热点，有着较高的理论研究与应用价值。
跳跃运动是腿型机器人的一种重要的运动方式，但是由于跳跃运动对于机器人有着高爆发性和变约束性要求，具有跳跃功能的腿型机器人是一个高度非线性、多变量、强耦合和变结构的复杂动力学系统，其驱动性能约束下的逾障规划和动态平衡控制的研究具有很大的挑战性。本文以电机和弹簧耦合驱动的平面腿型跳跃机器人为研究对象，考虑脚掌在起跳过程中绕脚尖发生转动，从提高机器人跳跃能力的角度，结合运动约束条件，对腿型跳跃机器人的动力学建模、跳跃步态生成、轨迹跟踪控制、落地稳定性等关键问题进行研究。
针对腿型跳跃机器人跳跃过程中与地面间的变约束特性，在考虑脚掌绕脚尖转动的情况下，采用Lagrange方程建立包括连续动力学模型和碰撞相离散动力学模型在内的腿型跳跃机器人混杂系统的动力学模型，通过对机器人被动关节的动态分析得出模型动态切换条件。
针对机器人规则地形下的跳跃运动规划问题，研究基于运动约束与最小能耗的平面腿型跳跃机器人稳定跳跃步态生成算法。该算法在考虑脚掌转动的情况下，分析完整跳跃周期中被动关节的表达式和机器人跳跃过程中所受到的运动约束条件，并基于最小能耗采用优化的思想进行平面腿型跳跃机器人稳定跳跃仿真试验。
针对具有不确定性干扰的腿型跳跃机器人系统模型，研究基于非奇异终端滑模控制率的轨迹跟踪控制问题。考虑腿型跳跃机器人跳跃过程中的实际因素，建立基于Simscape的系统模型并进行相关的仿真。
根据脚掌模型，分析存在脚掌转动的腿型跳跃机器人落地碰撞阶段的稳定性问题。存在脚掌转动的落地碰撞阶段腿型跳跃机器人系统稳定性问题是与该欠驱动系统零动态的稳定性相关。通过控制使系统输出为零，将零动态稳定性问题转化为系统闭环动力学方程的稳定性问题，得出存在脚掌转动的腿型跳跃机器人落地阶段的稳定性主要取决于机器人的结构参数和脚掌-地面接触面的性能参数。
本文有关平面腿型跳跃机器人的动力学建模、跳跃步态生成、轨迹跟踪及落地稳定性分析方法，有助于提高腿型跳跃机器人的灵活性和运动能力，拓展腿型机器人的应用领域，在理论和应用上都具有一定的借鉴作用和参考价值。
In recent decades, legged robot has become a hot spot in the field of research on mobilerobot, having a higher theoretical research and application value.
Hopping is an important way of movement for legged robot, but it requires that the robotis more explosive with variable restraint. As to the fact that hopping legged robot is a complexdynamic system which is highly non-linear, multi-variable, strong coupling and structurechanging, it becomes a challenging job to achieve obstacle negotiation planning and dynamicbalance control under driving performance constraints. Considering the planar hopping leggedrobot with the motor and spring coupling driver as the research object in this paper, and thepoint that the sole rotates by the tiptoe in the take-off phase and from the perspective ofimproving the hopping ability of the robot, the key problems containing dynamic modeling,hopping gait generation, trajectory tracking control and landing stability are discussed, withmotion constraints combined.
Considering the various constraints characteristics of legged hopping robot and solerotation, The hybrid system including continuous dynamic model and collision discretedynamic model is built, and the model dynamical changing conditions can be obtainedthrough research on the dynamic analysis of the passive joints.
Aimming at the hopping planning problems in inerratic terrain, the gait generationalgorithm of plane legged hopping robot is proposed. Considering sole rotating, the passivejoint expressions in the complete hopping cycle and the movement constraints in robothopping process are analyzed in this algorithm, and the test on the stable hopping simulationof the planar legged hopping robot is accomplished with optimized thought based on theminimum energy consumption. By the collision in hopping process and under-actuated statein take-off phase, it shows that under-actuated state in take-off phase may increase thetake-off speed effectively and improve the hopping performance, and that hopping withoutcollision could not be achieved considering the performance of the servo motor at present.
The legged hopping robot three-bar model with uncertain interference is taken intoconsideration and trajectory tracking controller based on the Nonsingular terminal slidingmode control rate is designed, demonstrating that the designed controller can track the expected trajectory in the limited time. Considering the practical factors of legged hoppingrobot in hopping process, the related simulation of the system model based on Simscape is putforward. The simulation results indicate the effectiveness of the trajectory tracking controllingalgorithm.
Based on the robot sole model, the collision stability problem of the legged hoppingrobot with sole rotation in landing phase is analyzed. The stability issues on the landingcollision in legged hopping robot system with sole rotation are related to the stability of theunder-actuated system zero dynamic. Through designing the zero output control rate inlanding phase, the zero dynamic stability problem can be transformed to that of theclosed-loop system dynamic equations. By the research on the closed-loop dynamic equationsand the landing stability parameters, it reveals that the stability problem of the legged hoppingrobot with sole rotation in landing phase depends largely on the structural parameters of therobot and the performance parameters of interface between the sole and the ground.
Analysis methods on the planar legged hopping robot dynamic modeling, jumping gaitgeneration, trajectory tracking and landing stability in this paper help improve the exerciseability and flexibility. Also, the methods expand the application areas of legged robot andhave certain reference value in the theory and application.
跳跃运动是腿型机器人的一种重要的运动方式，但是由于跳跃运动对于机器人有着高爆发性和变约束性要求，具有跳跃功能的腿型机器人是一个高度非线性、多变量、强耦合和变结构的复杂动力学系统，其驱动性能约束下的逾障规划和动态平衡控制的研究具有很大的挑战性。本文以电机和弹簧耦合驱动的平面腿型跳跃机器人为研究对象，考虑脚掌在起跳过程中绕脚尖发生转动，从提高机器人跳跃能力的角度，结合运动约束条件，对腿型跳跃机器人的动力学建模、跳跃步态生成、轨迹跟踪控制、落地稳定性等关键问题进行研究。
针对腿型跳跃机器人跳跃过程中与地面间的变约束特性，在考虑脚掌绕脚尖转动的情况下，采用Lagrange方程建立包括连续动力学模型和碰撞相离散动力学模型在内的腿型跳跃机器人混杂系统的动力学模型，通过对机器人被动关节的动态分析得出模型动态切换条件。
针对机器人规则地形下的跳跃运动规划问题，研究基于运动约束与最小能耗的平面腿型跳跃机器人稳定跳跃步态生成算法。该算法在考虑脚掌转动的情况下，分析完整跳跃周期中被动关节的表达式和机器人跳跃过程中所受到的运动约束条件，并基于最小能耗采用优化的思想进行平面腿型跳跃机器人稳定跳跃仿真试验。
针对具有不确定性干扰的腿型跳跃机器人系统模型，研究基于非奇异终端滑模控制率的轨迹跟踪控制问题。考虑腿型跳跃机器人跳跃过程中的实际因素，建立基于Simscape的系统模型并进行相关的仿真。
根据脚掌模型，分析存在脚掌转动的腿型跳跃机器人落地碰撞阶段的稳定性问题。存在脚掌转动的落地碰撞阶段腿型跳跃机器人系统稳定性问题是与该欠驱动系统零动态的稳定性相关。通过控制使系统输出为零，将零动态稳定性问题转化为系统闭环动力学方程的稳定性问题，得出存在脚掌转动的腿型跳跃机器人落地阶段的稳定性主要取决于机器人的结构参数和脚掌-地面接触面的性能参数。
本文有关平面腿型跳跃机器人的动力学建模、跳跃步态生成、轨迹跟踪及落地稳定性分析方法，有助于提高腿型跳跃机器人的灵活性和运动能力，拓展腿型机器人的应用领域，在理论和应用上都具有一定的借鉴作用和参考价值。
In recent decades, legged robot has become a hot spot in the field of research on mobilerobot, having a higher theoretical research and application value.
Hopping is an important way of movement for legged robot, but it requires that the robotis more explosive with variable restraint. As to the fact that hopping legged robot is a complexdynamic system which is highly non-linear, multi-variable, strong coupling and structurechanging, it becomes a challenging job to achieve obstacle negotiation planning and dynamicbalance control under driving performance constraints. Considering the planar hopping leggedrobot with the motor and spring coupling driver as the research object in this paper, and thepoint that the sole rotates by the tiptoe in the take-off phase and from the perspective ofimproving the hopping ability of the robot, the key problems containing dynamic modeling,hopping gait generation, trajectory tracking control and landing stability are discussed, withmotion constraints combined.
Considering the various constraints characteristics of legged hopping robot and solerotation, The hybrid system including continuous dynamic model and collision discretedynamic model is built, and the model dynamical changing conditions can be obtainedthrough research on the dynamic analysis of the passive joints.
Aimming at the hopping planning problems in inerratic terrain, the gait generationalgorithm of plane legged hopping robot is proposed. Considering sole rotating, the passivejoint expressions in the complete hopping cycle and the movement constraints in robothopping process are analyzed in this algorithm, and the test on the stable hopping simulationof the planar legged hopping robot is accomplished with optimized thought based on theminimum energy consumption. By the collision in hopping process and under-actuated statein take-off phase, it shows that under-actuated state in take-off phase may increase thetake-off speed effectively and improve the hopping performance, and that hopping withoutcollision could not be achieved considering the performance of the servo motor at present.
The legged hopping robot three-bar model with uncertain interference is taken intoconsideration and trajectory tracking controller based on the Nonsingular terminal slidingmode control rate is designed, demonstrating that the designed controller can track the expected trajectory in the limited time. Considering the practical factors of legged hoppingrobot in hopping process, the related simulation of the system model based on Simscape is putforward. The simulation results indicate the effectiveness of the trajectory tracking controllingalgorithm.
Based on the robot sole model, the collision stability problem of the legged hoppingrobot with sole rotation in landing phase is analyzed. The stability issues on the landingcollision in legged hopping robot system with sole rotation are related to the stability of theunder-actuated system zero dynamic. Through designing the zero output control rate inlanding phase, the zero dynamic stability problem can be transformed to that of theclosed-loop system dynamic equations. By the research on the closed-loop dynamic equationsand the landing stability parameters, it reveals that the stability problem of the legged hoppingrobot with sole rotation in landing phase depends largely on the structural parameters of therobot and the performance parameters of interface between the sole and the ground.
Analysis methods on the planar legged hopping robot dynamic modeling, jumping gaitgeneration, trajectory tracking and landing stability in this paper help improve the exerciseability and flexibility. Also, the methods expand the application areas of legged robot andhave certain reference value in the theory and application.
引文
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