Michael A. Erdmann

On multiple moving objects

This paper explores the motion-planning problem for multiple moving objects. The approach taken consists of assigning priorities to the objects, then planning motions one object at a time. For each moving object, the planner constructs a configuration space-time that represents the time-varying constraints imposed on the moving object by the other moving and stationary objects. The planner represents this space-time approximately, using two-dimensional slices. The space-time is then searched for a collision-free path. The paper demonstrates this approach in two domains. One domain consists of translating planar objects; the other domain consists of two-link planar articulated arms.

An exploration of sensorless manipulation

An autonomous robotic manipulator can reduce uncertainty in the locations of objects in either of two ways: by sensing, or by motion strategies. This paper explores the use of motion strategies to eliminate uncertainty, without the use of sensors. The approach is demonstrated within the context of a simple method to orient planar objects. A randomly oriented object is dropped into a tray. When the tray is tilted, the object can slide into walls, along walls, and into corners, sometimes with the effect of reducing the number of possible orientations. For some objects a sequence of tilting operations exists that leaves the objects orientation completely determined. The paper describes an automatic planner that constructs such a tilting program, using a simple model of the mechanics of sliding. The planner has been implemented, the resulting programs have been executed using a tray attached to an industrial manipulator, and sometimes the programs work. The paper also explores the issue of sensorless manipulation, tray-tilting in particular, within the context of a formal framework first described by Lozano-Perez, Mason, and Taylor [1984]. It is observed that sensorless motion strategies perform conditional actions using mechanical decisions in place of environmental inquiries.

Using backprojections for fine motion planning with uncertainty

This paper outlines a method for planning motions in the presence of uncertainty. Tasks are modeled as geometrical goals in configuration space. The planning process consists of determining regions from which particular motions are guar anteed to reach a desired goal successfully. An algorithm is presented for backprojecting from desired goal states. The backprojection regions are computed by erecting constraints that geometrically capture the uncertainty in motion. The relationship of backprojections to goal recognizability is discussed within the formal framework of preimages. This relationship suggests a partitioning of desired goal states into recognizable goal states. Backprojections are actually per formed from this partitioning.

On a Representation of Friction in Configuration Space

This article provides a geometric representation of friction for a rigid planar part with two translational and one rotational degrees of freedom. The article constructs a generalized friction cone by imbedding into the parts configuration space the force constraints that define the classic Coulomb friction cone in real space. The resulting representation provides a simple geometric method for determining the possible motions of a part subjected to an applied force and torque. The representation has been used both for simulating part motions and for planning assem bly operations. The approach generalizes to the six-dimensional configuration space of a three-dimensional part.

Motion sketching for control of rigid-body simulations

Motion sketching is an approach for creating realistic rigid-body motion. In this approach, an animator sketches how objects should move and the system computes a physically plausible motion that best fits the sketch. The sketch is specified with a mouse-based interface or with hand-gestures, which move instrumented objects in the real world to act out the desired behaviors. The sketches may be imprecise, may be physically infeasible, or may have incorrect timing. A multiple-shooting optimization estimates the parameters of a rigid-body simulation needed to simulate an animation that matches the sketch with physically plausible timing and motion. This technique applies to physical simulations of multiple colliding rigid bodies possibly connected with joints in a tree (open-loop) topology.

Understanding action and sensing by designing action-based sensors

This article proposes a method for automatically designing sensors from the specification of a robots task, its actions, and its uncertainty in control. The sensors provide the information required by the robot to perform its task, despite uncertainty in sensing and control. The key idea is to generate a strategy for a robot task by using a backchaining planner that assumes perfect sensing while taking careful account of control uncer tainty. The resulting plan indirectly specifies a sensor that tells the robot when to execute which action. Although the planner assumes perfect sensing information, the sensor need not ac tually provide perfect information. Instead, the sensor provides only the information required for the plan to function correctly.

An Exploration of Nonprehensile Two-Palm Manipulation

When two hands manipulate a part, they perform three basic opera tions : holding or rotating the part in an equilibrium grasp, allowing the part to fall in disequilibrium, and sliding one hand or the other relative to the part. This paper discusses a method for represent ing these primitive operations, focusing in particular on the sliding motions. The basic idea is to partition the combined configuration space of the part and palms into volumes of invariant contact me chanics. Within each volume, the possible motions of the part and palms are qualitatively equivalent. The precise accelerations may vary, but the contact mode is invariant. The possible part and palm motions are a function of the overlap of the contact friction cones with the line of gravity acting through the parts center of mass. A critical event analysis of this dependence allows the robot to parti tion the combined configuration space into the volumes of invariant contact mechanics. This system generates plans for manipulating the part by searching the resulting graph.

Mechanical parts orienting: The case of a polyhedron on a table

The positioning and orienting of parts is a standard problem in manufacturing. Orienting parts is often a prelude to the assembly of parts at tight tolerances. This paper considers the problem of orienting a part resting on a table, by tilting the table. The initial orientation of the part is assumed to be completely unknown. The objective is to tilt the table in a manner that reduces the uncertainty in the parts orientation. This paper focuses on three-dimensional polyhedral parts, with infinite friction between the parts and the table, and for which all transitions between different face-table contacts may be regarded as rotations across edges. The paper proposes a planner that determines a sequence of tilting operations designed to minimize the uncertainty in the parts orientation. The planner runs in timeO(n3), wheren is the number of faces of the polyhedron. The planner produces a sequence ofO(n) distinct tilting operations. Each tilting operation wobbles the table until the part is in steady state.

An Exploration of Nonprehensile Two-Palm Manipulation: Planning and Execution

This paper describes our current research into nonprehensile palm manipulation. The term “palm” refers to the use of the entire device surface during manipulation, as opposed to use of the fingertips alone. The term “nonprehensile” means that the palms hold the object without wrapping themselves around it, as distinguished from a force/from closure grasp often employed by a fingered hand. Indeed, nonprehensile operations such as purposeful sliding and constrained dropping constitute important palm primitives.

Randomization in robot tasks

This article explores the role of randomization in the solution of robot manipulation tasks. Randomization refers to the ran dom selection and execution of an action from a collection of possible actions. The intention is that this collection contains some actions that are useful for making progress toward ac complishing a task, but that the precise identity of these useful actions is unknown. Randomization offers one approach for ensuring progress in a probabilistic sense. An example of randomization is given by the strategy of shaking a bin containing a part in order to orient the part in a desired stable state with some high probability. Another exam ple consists of using reliable sensory information to bring two parts close together, then relying on short random motions to actually mate the two parts once the part motions lie below the available sensing resolution. Further examples include tapping parts that are tightly wedged, twirling gears before trying to mesh them, and vibrating parts to facilitate a mating operation. Randomization is also useful for mobile robot navigation and as a means of guiding the design process. Randomization is useful in three basic ways. First, random ization can increase the class of solvable tasks. This is because a randomized strategy need not guarantee task success with certainty in a specific number of steps, relying instead on re peated execution of the randomizing actions to accomplish the task in an expected sense. Second. randomization can reduce a strategys knowledge requirements. This is because randomiza tion can tolerate and circumvent local failures, thereby making a strategy less sensitive to task details. Third, randomization can simplify the planning and execution process. This is be cause a randomized solution may be able to ignore precise prediction of special case scenarios, instead simply ensuring eventual accomplishment of the task independent of the actual scenarios encountered.