Path Optimization for Humanoid Walk Planning - An Efficient Approach

This paper deals with humanoid walk planning in cluttered environments. It presents a heuristic and efficient optimization method that takes as input a path computed for the robot bounding box, and produces a path where a discrete set of configurations is reoriented using an A* search algorithm. The resulting trajectory is realistic and time-optimal. This method is validated in various scenarios on the humanoid robot HRP-2. 1 RELATED WORK AND CONTRIBUTION The problem of humanoid walk planning can be defined as follows: given an environment and a humanoid robot with start and goal placements, a collision-free trajectory needs to be found. It should ideally represent realistic human motion, i.e. a motion similar to that of a human being in the same conditions. This result is desirable since humanoid robots are bound to move in man-made environments such as homes, offices, and factories and because it can help them blend in among humans. 1.1 Humanoid Walk Planning The problem of motion planning is now well formalized in robotics and several books present the various approaches (Latombe, 1991; Choset et al., 2005; LaValle, 2006). Sampling-based methods rely on random sampling in the configuration space (CS) and use for instance Probabilistic Roadmaps (PRM) (Kavraki et al., 1996) or Rapidly-Expanding Random Trees (RRT) (Kuffner and LaValle, 2000). With these methods it is possible to solve problems for systems with large numbers of Degrees of Freedom (DoF). The motion planning problem is certainly a complex one in the case of humanoid robots, which are high-DoF redundant systems that have to verify Figure 1: Humanoid Robot HRP-2 uses holonomic motion, or side-stepping, to pass between two chairs. bipedal stability constraints. Various planning strategies can be found in literature. One category relies on whole-body task planning: kinematic redundancy is used to accomplish tasks with different orders of priorities (Khatib et al., 2004; Kanoun et al., 2009). Static balance and obstacle avoidance can thus be defined as tasks that the algorithm has to respect. Works of (Kuffner et al., 2001; Chestnutt et al., 2005) describe in particular humanoid footstep planning schemes. Starting from an initial footstep placement, they use an A* graph search (Hart et al., 1968) to explore a discrete set of footstep transitions. The search stops when the neighborhood of the goal footha l-0 05 72 37 5, v er si on 3 21 J un 2 01 1 step placement is reached. This approach is not practical in some environments with narrow passages, and (Xia et al., 2009) reduced the computational cost of footstep planning by using an RRT planning algorithm. Another strategy consists of dividing a highdimensional problem into smaller problems and solving them successively (Zhang et al., 2009). The idea of dividing the problem into a two-stage scheme is described in (Yoshida et al., 2008): A 36-DoF humanoid robot is reduced to a 3-DoF bounding box. Using the robot simplified model, the PRM algorithm solves the path planning problem and generates a feasible path for the bounding box. A geometric decomposition of the path places footsteps on it, and a walk pattern generator based on (Kajita et al., 2003) finally produces the whole-body trajectory for the robot. In (Moulard et al., 2010), this two-stage approach is also used; numerical optimization of the bounding box path produces a time-optimal trajectory that is constrained by foot speed and distance to obstacles. Another important issue is the notion of holonomic motion: while wheeled robots always remain tangent to their path, thus following a nonholonomic constraint, legged robots can also move sideways, and their motion can be described as holonomic. The path planning scheme in (Yoshida et al., 2008) is designed to this end; a PRM algorithm first builds a roadmap with Dubins curves (Dubins, 1957); but such curves impose a nonholonomic constraint and narrow passages cannot be crossed. The roadmap is therefore enriched with linear local paths. As a result this planning scheme generates motion such that the robot remains tangent to its path most of the time and uses sidestepping only in narrow passages. Furthermore, (Mombaur et al., 2010) conducted a series of walking experiments that allowed them to build a model of human walking trajectories; if a human being walks long distances, his body tends to be tangential to his path, while holonomic motion is used over smaller distances. This is an attractive property for computed paths if a realistic motion is to be achieved, and holonomic motion can as well be used to pass through narrow spaces. These results suggests that a good combination of both nonholonomic and holonomic motions can be used to achieve realistic walking.