Humanoid robots are expected to work in the human life environment. In real environment, there are unknown irregularities on the ground and unknown disturbances. It is required that humanoid robots realize motions with absorbing these unknown disturbances. In previous works, successful results have been shown by Trajectory Replay approach, in which the control problem is simplified by separating it into the referential pattern planning and the compensation of modeling error and disturbances. In order to put humanoid robots into practical use, however, there are a lot of problems that should be solved.

Biped locomotion is realized by manipulating a distribution of contact forces on left and right feet. In previous works, this contact force distribution is realized by manipulating Zero Moment Point (ZMP), which is the point of application of the total reaction force. There is a physical constraint on the contact force distribution, and this constraint changes as the contact region deforms. In order to achieve a robust biped locomotion, it is important how to synthesize 1) deformation of the contact region and 2) manipulation of the contact force distribution.

One of purposes of this dissertation is to improve a deformation capability of the contact region for mobility enhancement. While the force distribution specifies relative positional relationship of ZMP in the contact region, the contact region determines the manipulable limit of ZMP, in other words, how much COG acceleration is manipulable. Therefore, mobility enhancement is expected by enabling larger contact region to be achieved. Humans have evolved a foot mechanism specialized in biped locomotion. While foot structure of most existing humanoid robots is very simple, human can increase the effective length of the leg by utilizing toe joint. As a result, it is possible to increase a stride length or decrease knee joint velocity compared with walking on the flat sole. In this respect, a novel toe-thenar mechanism is proposed in Chap. 2. Although some researchers added 1 DOF toe joint to humanoid robots, the joint axis tends to become larger because a large radial load imposed on it. Proposed mechanism enables human-like multiple contact and force distribution on the toe and the thenar. Using this mechanism, the robot can support a major part of its weight on the thenar, and the radial load is decreased. Fig. 1 shows the developed toe-thenar mechanism for a miniature humanoid robot.In Chap. 3, we present a contact force distribution planning for a motion with toe contact phase. In biped locomotion planning, it is required to consider the discontinuous change of the contact region and the physical constraint depending on it. In particular, the change of contact region becomes more complex when the robot utilize toe contact phase. Extending the Boundary Condition Relaxation method, force distribution and COG pattern while the contact region changes from the sole to the toe is planned simultaneously. Fig. 2 shows snapshots of a walking motion including toe support phase which is planned with proposed method. Fig. 3 shows planned COG, ZMP and the change of the contact region, and ZMP is planned with the physical constraint satisfied. The left side of Fig. 4 shows loci of the knee and toe joint angles, and the right side shows loci of the knee joint angle velocities. Compared with the normal waking motion with the same stride length, the maximum joint velocities was deduced by about 40[%].

The second purpose is to compensate the error of the force distribution. The unknown irregularities on the ground cause an error from the planned contact force distribution. We propose a compensation method by adjusting leg impedance depending on each leg function in Chap. 4. Although the impedance control is efficient to compensate the effect of the ground irregularities, the desired characteristics of support and swing leg are different: the support leg is desired to be rigid to support the robot weight whereas the swing leg is desired to be flexible to absorb the touchdown impact and the error due to the irregularities. In proposed compensation method, the leg impedance is adjusted with the force distribution ratio. Fig. 5 shows snapshots of a walking experiment on the ground with 3[mm] height plastic plate. Applying the proposed impedance control with leg impedance adjustment, the robot carried out the total four steps walking without falling or body oscillation.

The third purpose is to absorb a disturbance by controlling the force distribution. It is required of the control of the force distribution to consider the physical constraint specified by the contact region. In Chap. 5, we specify state values without violating the physical constraint based on the maximal CPI (Constraint Positively Invariant) set assuming COG-ZMP inverted pendulum model. Furthermore, we apply the switching control of constrained systems and improve convergence speed of COG. We simulated initial responses with three different feedback gains. Fig. 6 shows the simulation results of each feedback gains (namely, without the switching control). Feedback gains were designed such that the gain becomes higher as its index becomes larger. When the feedback gain 2 or 3 were applied, the constraint of ZMP, which is indicated in the gray region in the figure, was violated. Simulation result applying the switching control is shown in Fig. 7. The feedback gains were switched at 0.75[sec] and 0.84[sec], and the convergence time is reduced from 2.4[sec] to 1.1[sec], by about 54[%].

Originally, the calculation of the maximal CPI set requires iteration of the linear programming. In biped locomotion, however, it is necessary to recalculate the maximal CPI set in real-time when the contact region changes after stepping. In Chap. 6, we present the recalculation method of the maximal CPI set. Furthermore, when a disturbance imposes on the robot, stepping motions to avoid falling are generated by detecting the stepping necessity based on the maximal CPI set. Fig. 8 shows snapshots of an experiment when the disturbance was imposed on the robot from back to front. The stepping necessity was detected and the robot stepped forward and COG was regulated to the center point of both feet after stepping.

Fig. 1 Toe-Thenar mechanism with parallel four-bar linkage

Fig. 2 Snapshots of the walking motion including toe support phase

Fig. 3 Planned COG and ZMP for walking motion including toe support phase

Fig. 4 Loci of the knee and toe joint angles, and the knee joint angle velocities

Fig. 5 Snapshots of walking experiment on the ground with a plastic plate. Applying impedance control, the robot carried out the total four steps walking motion.

Fig. 6 Initial response of the system. The left and right are response of COG and ZMP, respectively.

Fig. 7 Initial response of the system when switching control applied. At 0.75[sec] and 0.84[sec], controller switched the compensator.

Fig. 8 Snapshots when the disturbance was imposed on the robot from back to front. The stepping necessity was detected and the robot stepped forward.

本論文は「Study on Adaptive Contact Force Distribution of Humanoid Robots-Force Distribution in Toe-Thenar Mechanism and Impedance Distribution between Legs-」(ヒューマノイドロボットの接地力の適応的分配に関する研究―爪先・拇趾球間力分配機構と脚間イピーダンス分配制御―)と題し、7章からなっている。

ヒューマノイドロボットの二足歩行では、安定性の問題が一義的な問題となる。このような歩行安定性の問題については、与えられた運動軌道へのフィードバック制御を設計するもの、状況に応じて境界条件を満たすべく運動軌道を生成するもの、神経振動子を内蔵しそれによる引き込み現象を利用ることで安定化を図るもの、経験的に反射動作を作りセンサ信号に反応する動作を発生させるものなど、様々な方向からの研究がおこなわれてきた。一方で、ロボットの基礎要素であるアクチュエータの研究も進展してきており、接触力を精度よく制御することのできるバックドライバビリティをもつものの開発が進められている。本研究は、このような背景を鑑みて、ヒューマノイドロボットの両足あるいは片足支持期において接触力をどのように変化させるかという問題を適応的な力分配の問題として位置付け、接触力の分配の範囲を高めるための新しいつま先機構の設計からはじめ、力分配の計画、適応的な力分配制御、接触面に拘束された力分配、接触面の変化を考慮した力分配へと議論を展開してゆくことで、ヒューマノイドロボットの接地力の適応的な配分を行ない動的安定性の高性能化をはかることを目指した研究である。

本論文の第1章は序論で、はじめにヒューマノイドロボット自身と二足歩行に関する従来の研究を概観し、本論文で扱う力分配問題の学術的位置づけを行っている。

第2章では、力分配可能な領域である両足支持期の接地面積を広げ、歩幅を広く取ることができるように、新しい爪先機構をもつ足部の設計を行っている。足部は爪先と同時に拇趾球を持つ構造とすることで、ヒューマノイドロボットの体重を主に拇趾球で受けることができる。これによって、爪先部の力制御を精度良く行える、つま先支持部の強度を下げることで軽量化が図れるなどの特長をもつ。

第3章では、接触面をあらわす凸多角形において、いわゆるZMPを用いて爪先の自由度も考慮して接触圧力中心の移動を計画することを論じている。

第4章では、適応的な力分配制御法として、ZMPの位置に応じて脚のインピーダンスを変化させるインピーダンス・モジュレーションという考え方を提唱し、これによって接触時の衝突の影響を抑えながらも支持脚の剛性を高く保つことが、単純なアルゴリズムで機動的に行えることを示した。

第5章では、拘束システムを議論する正不変集合の理論を、接触領域の凸多角形拘束へ適用し、拘束を受ける制御系の安定化の問題に帰着させることができ、これによって収束速度を高めた安定化が実現できることを、シミュレーションと実験によって示した。

第6章では、踏み出しの際の接触領域の変化の際に、最大正不変集合を考慮した計算を近似することによってリアルタイムで行い、制御計を切り替えることで機動的で収束速度の高い安定化が実現できることを、シミュレーションと実験により示した。

第7章は、以上の研究の成果をまとめ結論を述べたものである。

以上を要するに、本論文は接触領域における力分配の問題としてヒューマノイドロボットの動的安定化の問題を議論し、爪先機構の開発から、接触力の変化の計画法、インピーダンス・モジュレーションによる衝撃の緩和、正不変集合理論を用いた収束速度の改善までを統一的に論じ、シミュレーションと実験によって有効性を明らかにしたものであり、知能機械情報学に貢献するところが大きい。

よって本論文は博士(情報理工学)の学位請求論文として合格と認められる。