Trajectory Generation for Mobile Manipulators

Mobile robot navigation has stood as an open and challenging problem over decades. Despite the number of significant results obtained in this field, people still look for better solutions. Some mobile robots are subject to constraints of rolling without slipping and thus belong to non-holonomic systems. Mobile robots also are subject to navigate in environments cluttered with obstacles. Now, in case the mobile robot presents a nonholonomic constraint, the problem consists of finding a path taking into account constraints imposed both by the obstacles and the non-holonomic constraints. Since non-holonomy make path planning more difficult, many techniques have been proposed to plan and generate paths. May be the most popular is the method of potential field (Khatib, 1986). However, this method may present some problems such as sticking to local minima. Moreover, the kinematic constraint is the other problem that can face trajectory planning. This can make time derivatives of some configuration variables non-integrable and hence, a collision free path in the configuration space not achievable by steering control.. Some researchers worked to find feasible path using different methodologies (Sundar & Shiller, 1997), (Laumond et al, 1994), (Reeds & Shepp, 1990). To deal with obstacles, some researchers decomposed the dynamic motion to static paths and velocity-planning problem (Murray et al, 1994), (Tilbury et al, 1995). In the work of (Qu et all, 2004), the authors treated the problem as a family of curves where the optimal path is found by adjusting a certain polynomial parameter. This idea was raised in many references including (Kant & Zucker, 1988) and (Murray & Sastry,1993), where trajectories are represented by sinusoidal, polynomial or piecewise constant functions. In our recent work, and based on intelligent control, we proposed a fuzzy control methodology to navigate a mobile robot in a cluttered environment with the aim to reach the goal while avoiding static and/or dynamic obstacles (Abdessemed et al, 2004). Concerning robot arm path planning and trajectory generation, considerable efforts have been devoted to make these mechanical systems succeeding in their tasks. If we consider a robot arm with n-joints that move independently, the robot’s configuration can be described by a 3-dimentional coordinate: (xe, ye, ze) for the location of the end effector. These coordinates characterize the workspace representation, since they represent exactly the same coordinates of the object it intends to manipulate or to avoid. Although the workspace is well suited for collision avoidance, it happens that we are still 15