以中樞模式發生器結合踏點力最佳化進行四足機器人之步態生成控制與變換

Abstract

在不平坦的地面上移動一直是在機器人領域中的一個重要議題，因為在地球上絕大多數的地表都是輪式機器人無法到達的。不過，在大自然當中，許許多多的動物都能輕易地征服這些地表。因此利用機器人效仿這些動物的移動方式，便是一個能讓機器人也有此等移動能力的明顯做法，而四足機器人便是在這個理念下誕生的產物。由於四足機器人的移動方式相當的複雜，四隻腳隨著出腳的順序與抬起落地的時間比例的不同，分成許多種步態。每種步態都有其所適合的地形與情境，若能夠讓機器人如同動物般，連續且自由的在不同的步態間進行變換，那麼就能使得機器人更好的適應不同地形之間的變換，使得讓機器人在使用上更有彈性。

本研究專注於設計能使得四足機器人得在步態之間連續平滑變換之控制系統，並保證在變換的過程中，不會出現其他之步態或觸地情形。為了使步態能夠連續的變換，使用中樞模式發生器輸出代表各腳抬起落地時間順序之週期性相位訊號。利用中樞模式發生器其極限圈的特性，變換極限圈就能透過連續動態系統之特性使步態連續且平滑的變換。本研究所提出之中樞模式發生器分為三個部分，振盪器，協調器與位能牆。振盪器產生週期性訊號，協調器負責動態耦合，位能牆則是阻止不穩定步態的出現。若機器人在一步態之觸地情形筆直站立，足尖皆落於髖關節之正下方，重心在地面之投影並不落在踏地點所形成之區域或連線中，則視該步態為不穩定之步態。若重心之投影不落在踏地點所形成之區域或連線中，重力會以踏地點為支點，形成一個無法以各腳出力抵銷之力矩，造成機器人翻倒。經由數值模擬與實際實驗，本研究所提出之中樞模式發生器能夠在步態變換時有效避開這些不穩定步態。

只決定步態並無法使機器人移動。配合線性化離散三維剛體做為機器人之動力學模型，將各腳與地面間之作用力作為系統輸入，機身之位置、速度、姿態與角速度做為系統輸出，利用最佳化的方式在系統表現與效率之間權衡，並考慮作用力方向與摩擦力等物理限制，求得最佳之系統輸入。再來，利用最佳系統輸入，推算下一刻機器人之理想狀態後，計算各腳足尖所需移動至的位置，進而控制機器人的機身狀態，穩定機身的位置與姿態。

在不穩定的步態外，有兩種常用的步態，行走與快步。行走為同時三腳著地之步態，理想上任何時刻皆為靜穩定。快步步態則為交叉之兩對腳交替落地之步態，並非靜態穩定的步態。為了使機器人能在快步步態下穩定向前，利用線性倒單擺模型作為依據進行踏點規劃，使得在快步步態下能動態穩定的向前移動。

最後，在本實驗室所開發之新型輪角複合四足機器人上，實際驗證本研究所提出之控制系統。結果顯示本研究所提出之控制系統能夠有效控制機身之狀態，並在行走與快步兩種步態間進行連續且穩定的步態變換。

Locomotion through uneven terrain has always been a main focus in the field of robotics. Since most of the land on earth is unreachable by wheels but can easily be conquered by animals, imitating the animals becomes an obvious method of obtaining such a capability. Quadruped robots were born under this concept and have been proven to be an effective solution by the hard work of many research teams in recent years. Due to the fact that the locomotion of quadruped robots are quite complex, different sequences of stepping legs and different stance-swing ratios divides into numerous kind of gaits. Each gait is suitable for different terrains and situations, thus if we can make the robots to be able to change the using gait freely and continuously like a living animal, then it can better adapt to the transition of different terrains, increasing the flexibility of the robot.

This study focuses on designing a novel control system that enables a quadruped robot to continuously and smoothly change between these two gait patterns, and ensures that no other unstable gait or grounding occurs during the transition. In order to change the gait continuously, a central pattern generator is used to output a periodic phase signal representing the swing and stance of each foot. Using the limit circle characteristic of the central pattern generator, it is able to achieve continuous and smooth transition of different gaits. The central pattern generator consists of three major parts, oscillator, synchronizer and potential wall. The oscillator generates the periodic signal, the synchronizer is responsible for the dynamic coupling of the phase signals, and the potential wall prevents the appearance of unstable gaits. If a robot is standing straight under the contact scenario of a gait, the projection point of the center of mass on the ground does not locate inside the support polygon or the support line constructed by the feet on the ground, then the specific gait is considered to be unstable. This is due to the gravity would form a torque that cannot be offset by the legs, and makes the robot fall. With numerical simulations and experiments, the proposed central pattern generator is guaranteed to avoid the unstable gaits during the transition of gaits.

However, only determining the gait is not sufficient for stable locomotion of the robot. Using linearized three-dimensional rigid body model as the dynamic model of the robot and treating contact forces between the feet and the ground as the system input. States such as position, velocity, orientation and angular velocity are regarded as system output, optimization techniques can be utilized to calculate the optimal system input, weighting between system performance or efficiency and with respect to physical constraints such as friction. Furthermore, since the system output of the next time step can be obtained by the result of optimization, the position of the legs can also be calculated using the system output. With the position of the legs, the robot can be controlled and stabilized. As the trotting gait is not a statically stable gait, foothold planning of each foot is added by considering the robot as a linear inverted pendulum, this allow the robot to be dynamically stable under both the trotting gait and the walking gait.

At last, the proposed control system of this work is tested and validated on a real quadruped robot. The results shows the proposed control system is able to control the states of the robot and achieve stable continuous transition between walking and trotting.