Dynamics and control of collision of multi-link humanoid robots with a rigid or elastic object

The main objective of this dissertation is to understand how the humanoid organisms or machines use appropriate control strategies and reference motions to achieve the desirable collision responses such as the contact time, the contact forces, the departure velocities of two colliding subjects and the physical deformation. Thereby, the collision of a subject with a rigid object such as a flat ground or a soft object such as a soccer ball is modeled and studied. Collision is a challenging task and involves coupling, motion planning, dynamics and controls. In particular, we are interested in the collision of a humanoid organism with a ground in the step stance. This collision involves the interaction between the two rigid objects. The equations of motion of a five-link three-dimensional subject embedded in a space larger than the joint space of the system are developed by sequential elimination, orthogonality of the spaces and virtual work mechanism, and then are projected onto the sagittal plane. The model is further projected onto the joint space where we obtain a tenth-order under-actuated system with the maximal number of three outputs that can be regulated. To avoid tackling such a system with complicated internal dynamics, finally, we project the joint space model onto the subspace whose dimension is equal to the number of degrees of freedom of the system. Inverse kinematics is used to map the Cartesian space to the joint space. Contact forces are formulated as the functions of the state variables and the controls. The step stance ii leap motion is considered in four phases: the take-off phase, the flight phase, the landing phase with impacts, and the standing-up phase. We also believe that human central nervous systems have the internal tendency and ability to seek to control the minimal number of state variables with minimal energy consumption during postural activity. Thus, control balance of the step stance of a subject after landing is simulated without prescribing the entire trajectory. Last, the under-actuated model is used to simulate the step stance takeoff of a subject. Collision of a subject with a soft object is studied by the interaction of a human rigid lower limb with a soccer ball. A general coupling model between the foot and the ball is obtained as a nonlinear spring in parallel with a nonlinear damper. Elasticity is estimated from experiment data by least square technique. Nonlinear damping in proportion to a restitution-related constant eliminates impact discontinuity. Contact force is modeled as a function of the penetration and penetration rate of the ball. Collision time between two objects can be as short as several milliseconds. Fast tracking convergence and small steady state tracking error are required in numerical simulation. For the step stance leap, an integral sliding mode control strategy is designed to track the reference motion, obtained by experimental recording of humans executing the step stance leap. It eliminates the reaching phase for the sliding mode. The stability, finite-time convergence and robustness of the systems are studied, proved and verified by computer simulation. The sliding mode control algorithm is developed to track the preplanned trajectory against modeling uncertainties and impact disturbances for the ball-foot interaction. The experiments are emphasized in this research. For the step stance leap, the predicted GRF profiles are in agreement with experimental recording of the GRFs. iii In particular, the predictions capture the short duration and large amplitudes of the GRFs upon impact as well as the burst of high energy required during the takeoff phase. For the ball-foot collision, the collision duration, the ball’s departure velocity, the average ball-foot collision force and the ball’s peak deformation obtained by simulation match the reported results. The observed three phases of the ballfoot collision are confirmed by our simulation. The “follow-through” phenomenon in sports is also demonstrated.