Development of Musculoskeletal Legs with Planar Interskeletal
Structures to Realize Human Comparable Moving Function

When the planar interskeletal structure contacts with the spherical skeletal structure, it can fit the skeletal structure by changing its path to transit to a lower energy potential state. This characteristics of the planar interskeletal structure keeps the skeletal structure inside of its surface. However, the skeletal structure under the linear interskeletal structures can easily deviate from them. When the joint deviates from the linear interskeletal structure, it is hard to support or control the joint by ligaments or muscles [7]. On the other hand, the planar interskeletal structure can stably transmit the muscle tension to the joint because it can maintain the planar contact with the skeletal structure even if the joint angle changes.

The linear interskeletal structure has small contact areas and is often caught in roughness of skeletal structures. This phenomenon increases involuntary tension between tendons in linear interskeletal structures, and therefore forcibly causes the change of muscle path and increases friction. Compared to linear interskeletal structures, planar interskeletal structures have large contact surfaces with skeletal structures and cover skeletal structures by their surfaces. This feature prevents the planar interskeletal structure from being caught in the folds of skeletal structures.

The linear skeletal structure can handle force in the pulling direction by its elasticity on the condition of being fixed by their position (rotationally free), but can hardly handle force in the orthogonal direction. Therefore the planar muscle [7], which is simply constructed by parallel muscles, cannot produce high power in the shear direction. On the other hand, we expect the planar interskeletal structures to handle force in the shear direction by interfering with fibers. We model the elasticity of planar interskeletal structures as a cluster of fibers and compares it with some liner interskeletal structures. Fig. 3 shows schematic diagram of skeletal structures.

Breen, et al. modeled the precise model of woven cloth based on the minimization of energy [8]. However, in this study, we model woven cloth as truss structure which is tracked by parallel and crossed wires (as shown in parallel-cross in Fig. 3), to consider external forces in only two directions on surface. The model which is tracked by parallel wires (Fig. 3 parallel) and the model which is pulled by crossed wires (Fig. 3 cross) will be compared with the planar-coss model. We assume that the tension and the elongation of wires have the following relationship.

$$T=\exp(K\max(0,(l-l_{0})-l_{d}))$$

(1)

${T}$ is the tension and ${K}$ is the stiffness of wire. ${K}$ is multiplied by the difference of current length of wire ${l}$ and equilibrium length of the wire ${l_{0}}$. We modeled it so that the tension of the wire develops according to the exponential function as the wire elongates. The tension develops only when the wire elogates over the constant elongation. The dead-band of the each wire is setted in $(-\infty,l_{d}]$. We set ${K=1.0}$/mm, ${l_{d}=0.5}$mm. ${l_{0}}$ is calculated based on the assumption that mounting points are 200mm away in the direction of ${y}$ axis in Fig. 3, 20 mm away in ${x}$ axis. On the condition that each structure has 4 wires, the result is shown in Fig. 4. It shows that parallel-cross structure can bear the force of the shear direction more than parallel structure and cross structure. In addition, this result shows that three sutructures have almost same durability in the pulling direction, but parallel-cross structure is a little stronger than cross structure in the pulling direction. Parallel structure is most strongest in the pulling direction. However, in order to use the advantage of merits described in II-A and II-B, planar structure which is modeled as parallel-cross sturucture is necessary, because linear sturcture cannot use the advantage of these merits.

The actual elasticity of each model against shear force was verified in an experiment using wires by Dyneema. An overview of the experiment is shown in 5. In this experiment, the wires were attached in such a way that restoring force was generated for the yaw degree of freedom of the knee joint as described in IV-B. In addition to the three wire attachment settings, a planar structure made of cloth was added for comparison. The results of the experiment are shown in 6. The result shows similar tendency to the simulation result. Although it is not possible to simply compare wires and a cloth because of the different materials and attachment methods, the planar structure made of a cloth is superior to the wire in terms of elasticity.

In this research, we developed the musculoskeletal humanoid legs MusashiOLegs (Fig. 7) as a successor of the musculoskeletal humanoid Musashi [9]. MusashiOLegs has 3 DOF in the spine joint, 3 DOF in the hip joints and 2 DOF in the knee joints. Each joint are constructed with pseudo spherical joints [9]. We show the overview and the muscle arrangement of MusashiOLegs in Fig. 7. The skeletal structures are drived by the contraction of the muscles (BLDC motors wind the chemical fiber Dyneema) [10]. It has 40 actuators as muscles, and some wires are folded back to gain enough torque with relatively few actuators.

This section discusses the requirements of applying the interskeletal planar structure to humanoid robots. We classify the interskeletal structures into two types; the passive planar interskeletal structure and the active planar interskeletal structure. The passive planar structure cannot produce force by itself and only transmit force to the other body parts like ligaments. The active planar structure exists in actively drivable body parts such as muscles.

In this subsection, we discuss the application of planar interskeletal sturcture to the musculoskeletal humanoid. First, we describe the two passive planar interskeletal structures; iliofemoral ligaments and knee collateral ligaments. Next, two active planar interskeletal structures is described; pattella ligaments and gluteus maximus.

First, we will confirm that the iliofemoral ligament made of the elastic planar interskeletal structure can softly restrict the range of motion. In the human body, when a human moves the femur towards the backside of the body, tension is applied to the iliofemoral ligament and the iliofemoral ligament restricts the extension axis of the hip joint. This restriction makes the pelvis and the femur move together. We confirm that the hip joint of MusashiOlegs has the same function.

The external force is applied to the femur in both directions of extension and bending, on the condition of the trunk of the body being suspended. In order to evaluate the passive torque in the hip joint applied by the ligament, muscles around the pelvis are slackened. The result of this experiment is shown in Fig. 13. In Fig. 13, spine-p, rhip-p, lhip-p represent the joint angle of the spine pitch, rleg hip pitch and lleg hip pitch. When the hip joint is bent, the joint angle of the spine does not change. However, when the hip joint is extended, the passive torque by the iliofemoral ligament locks the hip joint and the joint angle of the spine changed.

In this experiment, we confirm that the screw-home movement in the knee joint is realized by the passive torque generated from the planar collateral ligament. The screw-home movement is the function of the planar collateral ligament. The ligament allows complex rotational movement in knee flexion configuration, but the ligament locks the range of angle and stabilizes the knee joint in knee extension configuration. The previous research realized screw-home movement by the only rigid mechanism [14]. However, this mechanism cannot handle the impact force in the knee extension configuration and can break irreversibly. Not only the realization of a complex range of motion but also the soft restriction which can absorb impact force is important. We will show that the planar interskeletal structure implemented in III-C2 can satisfy these characteristics.

The schematic diagram of the knee joint attached to the collateral ligament and muscles is shown in Fig. 14. The collateral ligament is attached to the skeletal structure over the pseudo spherical joint which has 2Dof in yaw and pitch axis in Fig. 14. The quadriceps extend the knee joint. The collateral ligament should be attached to the skeletal structure of the thigh, because the screw-home movement is also the effect of the quadriceps. In this study, to evaluate only the effect of passive torque by the collateral ligament, the knee joint was fixed so that the quadriceps do not generate screw torque.

In these conditions, we set the knee joint bent and screwed randomly and extend knee joint using muscle actuators. Fig. 15 shows the result of 10 trials of extension of the knee joint from the randomly screwed configuration. This figure shows that the yaw joint angle of the knee joint converged to $0$ deg as the knee extends. As shown in Fig. 16, when the screwed knee joint extends, we observe that the screw-home movement by the passive torque of the collateral ligament locked the rotational axis of the knee joint as the knee joint extends.

We conducted a squat motion experiment to show that the musculoskeletal humanoid legs with planar interskeletal structures can perform high torque in a wide range of motion. In this experiment, muscles must maintain a moment arm to support the body weight of humanoid legs in a wide range of motion. We send muscle length direction to each muscle actuators using learned body image [15] which maps muscle length to joint angles.

We show the result of the experiment in Fig. 17 and Fig. 18. The musculoskeletal humanoid without the planar interskeletal structures [16] could not perform the squat motion, because it could not apply sufficient torque to joints. On the other hand, the musculoskeletal legs with the planar interskeletal structures achieved deep squat motion from the state {${hipjoint,kneejoint:64.7,112.3}$} ${[deg]}$.

Finally, we conducted the pedal switching experiment as environmental contact situation. In the pedal switching experiment, muscles must maintain the moment arm to transmit sufficient torque to each joint in tight postures. Also, the musculoskeletal legs must perform the task under friction with the car seat. In this experiment, the musculoskeletal legs is required to, first press the accel pedal, second put its foot away from the accel pedal, third move its foot to the above position of the brake pedal and finally press the brake pedal. The car used in this experiment is B.COM Delivery of extremely small EV COMS series. We send muscle-length direction to each muscle actuator using learned body image [15] which maps muscle length to joint angles.

The experimental appearance is shown in Fig. 19. In addition, Fig. 20 shows the appearance from the view above feet and Fig. 21 shows the foot force sensor data during the experiment. In previous research, the musculoskeletal humanoid pressed pedals using one leg for each pedal; the left leg for the brake pedal, and the right leg for the accel pedal [17]. This was because that the musculoskeletal humanoids could not produce enough torque to raise each leg in a seated situation. On the other hand, the musculoskeletal humanoid legs with planar interskeletal structures achieves pedal switching by single-leg like a human being. It can produce enough torque to raise the leg in the seated situation desptie friction between the car seat and the body.