Horizontal motion planning for multi-legged robots

Abstract

Solving legged robot navigation problems is challenging because of the robots' locomotion limitations and its complex kinematics and dynamics. Generic locomotion models for the legged robots such as the Spring Loaded Inverted Pendulum (SLIP) and the Lateral Leg Spring (LLS) involve masses, accelerations and second-order differential equations. Common path planning methods such as the Probabilistic Roadmap (PRM) and the Rapidly-exploring Random Tree (RRT) have their own limitations. Both of them typically assume that the robots do not have any kinematic limitations. In addition, RRT and PRM are open-loop, and as such, they do not produce the feedback strategies that correct when the robot is away from the desired path. Consequently, re-planning is practically required for implementations of the RRT and PRM. ☐ Templates are simplified models that capture salient features of robot motion behavior. The SLIP and LLS are considered templates. Karydis et al. provides a new locomotion template: the Switching Four Bar Mechanism (SFM) for legged robots. The SFM gives a static map between model parameters and robot displacement, and models the robot's motion without differential equation. On the other hand, the SFM offers the robot's configuration in closed form. The number of variables of the SFM can be reduced to one. ☐ In this thesis, we derive the inverse kinematics of the SFM, which maps the robot displacement to model parameters. We also provide a method for solving the problem of legged robot navigation in a way that provides feedback strategies in cluttered planar environments. This is achieved by combing the SFM as the locomotion template for the legged robots with navigation functions for motion planning. In this way, an existing, multi-variable, probably correct motion planning method, is transformed into a tractable single-variable. Locomotion-specific optimization algorithms are applied to our navigation method and are adjusted to hit a trade-off between efficacy and processing speed. Because our method provides feedback strategies, re-planning is not required. We provide some convergence conditions for our navigation method so that we can ensure that motion plans are always safe with regards to collisions with environmental boundaries. In conclusion, this thesis provides an approach that can be used for solving the planar navigation problem for robotic vehicle systems with kinematics given in closed-form.