Motion Planning Challenges

Advances in motion planning methods and algorithms have had a difficult time keeping up with growth of complexity of many current systems or situations. For instance, med- ical practitioners could make use of a deforming catheter-like robot to aid in performing various procedures. Related simulations could also help as a teaching tool or for preoper- ative planning. Hyper-redundant robots such as snake-like robots or self-reconfigurable modules may contain hundreds or possibly thousands of links and joints. Fleets of mo- bile robots sizing from the tens to hundreds are already used for managing warehouses. Autonomous vehicles will need to know how to avoid and navigate among many other moving obstacles. Virtual reality developers can populate their environments with many agents each of which have their own goal, task, or behaviors. All of these examples are very difficult to handle in the current state of motion planning algorithms.

The complete robot motion planning problem has been shown to be exponential in number of DOFs of the robot [Rei79,Can88b]. As previously mentioned, many modern and popular approaches employ randomization to quickly generate an approximate and hopefully representative mapping of theC, and they also relax the completeness require- ment in the process. These algorithms have enjoyed a great deal of success over the last decade due to their ability to solve a wide variety of problems in higher dimensional, or high DOF, configuration spaces in a more practical amount of time. Moreover, these randomized algorithms are generally intuitive and relatively easy to implement.

As the complexity of the robot or its environment increases, motion planning becomes more and more difficult. When considering problems with deformable robots, highly articulated robots, or multiple, complex robots such as those previously mentioned, the effectiveness of most motion planning algorithms rapidly deteriorates. By nature of randomized algorithms, the motion itself may not be even be realistic. Most of these approaches generate motion by linearly interpolating between states rather than preserving any kinematics, dynamics, or differential constraints. As a result, the motion

is not necessarily physically plausible, is not smooth, or may contain motion paths which are un-intuitive. There are some approaches which plan in the “state” space of a robot, sometimes referred to as “kinodynamic” planning [HKLR02]. However, since kinematic and dynamic constraints increase the dimensionality of the space which needs to be searched, they typically do not scale well to higher DOF planning scenarios.

Based on these considerations, we identify three important sources of complexity in motion planning for realistic, and more generic, scenarios:

1. Agent complexity: The complexity is inherent to the robot itself or to its ge- ometry. For instance, for a highly articulated robot with thousands of joints and possibly many branches or kinematic loops, the C has an extremely high dimen- sionality. As mentioned in Sec. 1.1.3, for a completely deformable robot theC may be intractably large. In both cases, the complexity of the robot is typically too great for standard planning approaches. Finally, to ensure smooth and realistic motions, dynamics and kinematics for these robots should be considered. Since each parameter in the “state” space adds additional DOFs to the problem, these constraints can also greatly increase the overall problem complexity.

2. Numerous agents: Many real world and virtual planning situations include multiple moving bodies, or multiple agents. A complete, centralized approach to this situation treats the DOFs of all the robots as a single robot, i.e. a single configuration describes the complete position and orientation of all robots and their sub-parts. Under this formulation, the problem is identical to the single- robot planning problem and can be handled as such (via any of the approaches mentioned earlier). Since the number of DOFs grows linearly with the number of robots, the inherent complexity of the planning problem becomes intractable with just a few robots. Decentralized approaches treat each robot individually; they plan for each robot individually and then perform a coordination planning step to try to ensure that robots do not collide as they execute their paths [KZ86,OLP89].

The latter solution is usually faster, but gives up the completeness property of a centralized algorithm and in practice has been shown to have a much lower success rate [SI06].

3. Dynamic environments: Finally, in many cases, there are other obstacles or items which are moving or are otherwise changing during the execution of the motion. These dynamic events and environments add complexity to the planning situation itself, and present additional challenges. In cases where the motion of obstacles is unpredictable, it adds a real-time constraint. The robot has a finite amount of time to decide how to avoid or adapt to a changing environment. In many cases, this requires the robot to quickly re-plan or otherwise adapt its current plan. Since planning is already a complex task, this poses a large challenge for even moderately complex environments. When the obstacle motion is known a priori, this adds a temporal dimension toC which makes planning more computationally expensive due to the larger search space.

In many real and virtual world situations, many of these constraints may exist even in a single situation or scenario. For instance, a city scene may include navigating agents which must also avoid moving vehicles. While algorithms do exist which can appropriately handle for each of them individually, the ability to do this successfully and in a reasonable amount of time diminishes as the problems become more complex. Even for moderately “realistic” problems, most modern motion planning algorithms tend to take a long time or do not respond in a practical amount of time.