# Whole-Body Motion Planning for a Six-Legged Robot Walking on Rugged Terrain
## 1 Introduction  
Over the last few decades, six-legged robots seem to have received much attention for several reasons. First, six-legged robots are useful scientific tools that can be employed to investigate complicated biological mechanisms such as biomechanics and neuroscience, on the side of biology, and planning and control algorithms, on the side of robotics [1; 2; 3; 4; 5]. Second, six-legged robots can be used in many application scenarios like search and rescue [6; 7]. As a result, to date a variety of six-legged robotic platforms have been constructed. Locomotion in complex terrain is one of the fundamental topics for legged robotic research. Broadly, various strategies adopted in the literature may be categorized into different approaches. The first is an executing-reacting approach which means the robot executes its predefined motions first then adapts to terrain changes through reactive behaviors. An example in this approach is the RHex-like robots which employ special-designed curved legs to achieve robust locomotion in rugged terrains [8; 9]. Such designs are simple, reliable and able to mechanically adapt to a certain degree of terrain roughness. Further, a number of legged robots integrate various control strategies to actively adapt to rugged terrain. Impedance control and posture control are two commonly used strategies in this line [6; 10; 11]. A number of six-legged robots also integrate different reflexes, including stretch reflex, searching reflex, stepping reflex, and elevator reflex, to react to obstacles or holes during stepping motions, thereby increasing the robot mobility on unstructured terrain [6; 11; 12; 13]. An alternate approachis a planning-reacting paradigm, which means reasonable motion would be deliberately planned before robot executing and additional terrain uncertainty would be overcome by reactive motion control. For example, [PERSON] and [PERSON] propose a Bezier curves based path planning method, which enables a quadruped robot to generate a feasible path in an obstacle-strown environment [13]. Likewise, in [14], the authors label the obstacles as accessible or inaccessible regions and then plan path for a legged robot by employing the potential field algorithm. A recent example is the BigDog quadruped robot, in which an optimal path was found using 2D cost map and A \({}^{*}\) algorithm [15]. On this basis, the planned path is commanded to be followed using robustly reactive motion controllers. With these approaches, robotic legged locomotion can be accomplished over moderately rugged terrains. Similar to human rock-climbing, whereby the climber has to carefully plan his/her foot/hand motions according to the rock wall and his/her capability, over severe rugged terrains, deliberate whole-body motion planning has to be conducted for legged robots. In addition, careful whole-body motion planning is also helpful for legged robots to address the limitations of its own kinematics, for example, a better kinematic margin for subsequent robot movements. In this line, [PERSON] et al. proposes two-layered whole-body motion planning for the six-legged robot Messor according to surrounding environment models. The authors use a higher-level planner, which uses A \({}^{*}\) algorithm to plan a path, and a lower-level planner, in which the guided-RRT is applied to find feasible motion trajectories of 18-dimensional joint space [7]. [PERSON] et al. employs a combination method of planning and optimization for a quadruped robot walking dynamically over rugged terrains [16; 17]. The trajectory of the robot CoG is generated by a series of quintic spline curves. The trajectory of the robot torso is given by optimizing squared accelerations along the trajectory based on the zero-moment point (ZMP) stability criterion. The foot trajectories are initially generated according to the convex hull of the terrain from the start location and the target location using piece-wise quintic splines, and then subsequently optimized to eliminate potential shin or knee collisions. [PERSON] et al.