First Steps Towards Full Model Based Motion Planning and Control of Quadrupeds: A Hybrid Zero Dynamics Approach The hybrid zero dynamics (HZD) approach has become a powerful tool for the gait planning and control of bipedal robots. This paper aims to extend the HZD methods to address walking, ambling and trotting behaviors on a quadrupedal robot. We present a framework that systematically generates a wide range of optimal trajectories and then provably stabilizes them for the fullorder, nonlinear and hybrid dynamical models of quadrupedal locomotion. The gait planning is addressed through a scalable nonlinear programming using direct collocation and HZD. The controller synthesis for the exponential stability is then achieved through the Poincare sections analysis. In particular, we employ an iterative optimization algorithm involving linear and bilinear matrix inequalities (LMIs and BMIs) to design HZDbased controllers that guarantee the exponential stability of the fixed points for the Poincare return map. The power of the framework is demonstrated through gait generation and HZDbased controller synthesis for an advanced quadruped robot, xe2x80x94Vision 60, with 36 state variables and 12 control inputs. The numerical simulations as well as real world experiments confirm the validity of the proposed framework.

Multicontroller multiobjective locomotion planning for legged robots Different legged robot locomotion controllers offer different advantages; from speed of motion to energy, computational demand, safety and others. In this paper we propose a method for planning locomotion with multiple controllers and subplanners, explicitly considering the multiobjective nature of the legged locomotion planning problem. The planner first obtains body paths extended with a choice of controller or subplanner, and then fills the gaps by subplanning. The method leads to paths with a mix of static and dynamic walking which only plan footsteps where necessary. We show that our approach is faster than pure footstep planning methods both in computation (2x) and mission time (1.4x), and safer than pure dynamicwalking methods. In addition, we propose two methods for aggregating the multiple objectives in searchbased planning and reach desirable tradeoffs without weight tuning. We show that they reach desirable Paretooptimal solutions up to 8x faster than fairlytuned traditional weightedsum methods. Our conclusions are drawn from a combination of planning, physics simulation, and real robot experiments.