Task and Motion Planning (TAMP)

The high-level reasoning layer that decomposes a complex goal into a sequence of discrete, symbolic actions. It operates on an abstract representation of the world using formal logic (e.g., PDDL) to satisfy preconditions and postconditions.

• Input: A goal state (e.g., "block A on block B").
• Process: Searches a space of possible action sequences.
• Output: A plan skeleton like [Pick(A), Place(A, B)].
• Key Challenge: Ensuring the symbolic plan is geometrically feasible for the low-level motion planner.

The low-level geometric layer responsible for computing collision-free, kinematically feasible paths for the robot's joints and end-effector between configurations. It translates symbolic actions into continuous motion.

• Operates on: The robot's configuration space (C-space) and a 3D model of the environment.
• Algorithms: Sampling-based planners (RRT*, PRM) or optimization-based methods (TrajOpt).
• Key Function: For a symbolic action Place(A, B), it computes the precise arm trajectory to move object A to a stable pose on top of object B, avoiding all obstacles.

The critical integration layer that grounds abstract symbolic actions in concrete geometric parameters. It is the primary source of complexity in TAMP, as it must resolve the interleaving of discrete and continuous planning.

• Function: For each symbolic action, it must find motion parameters that satisfy both logical and geometric constraints.
  • For Pick(obj): Find a stable grasp pose for the gripper on obj.
  • For Place(obj, loc): Find a stable placement pose for obj at loc.
• Mechanism: Often uses sampling or optimization to propose candidate parameters (grasps, poses) that the motion planner then tests for feasibility.

The feasibility checks that bind the entire system, ensuring plans are physically executable. These constraints are evaluated during the symbolic-geometric interface phase.

• Kinematic Constraints: Robot joint limits, reachability of a target pose.
• Collision Constraints: The robot, held object, and trajectory must avoid obstacles.
• Dynamic Stability: For mobile manipulators, actions must not tip the base.
• Grasp Stability: Computed contact forces must resist gravity and inertial forces.
• Task Constraints: Specific requirements like maintaining an object's orientation (e.g., not spilling a cup).

The overarching algorithm that orchestrates the search for a feasible task-and-motion plan. Pure sequential planning (task then motion) fails due to geometric infeasibility. TAMP requires interleaved search.

• Common Paradigms:
  • Hierarchical Planning: The task planner proposes a skeleton; the motion planner attempts to ground it, requesting alternative skeletons if it fails.
  • Sampling-Based TAMP: Algorithms like Focused Belief Tree Search sample both discrete actions and continuous parameters (grasps, poses) simultaneously in a single search tree.
• Goal: To find a plan where every symbolic action has a corresponding, feasible motion trajectory.

The system's belief state, which must be tracked and updated across both symbolic and geometric domains. It is the shared source of truth for all planners.

• Symbolic State: A set of logical predicates (e.g., On(A, Table), HandEmpty). Updated after each discrete action execution.
• Geometric State: The 6D poses of all objects and the robot, often provided by perception systems (e.g., 6D pose estimation from a vision system).
• Critical Role: The motion planner's success depends entirely on the accuracy of this geometric world model. Uncertainty in object pose is a major research challenge, leading to belief-space TAMP.

In a dynamic e-commerce warehouse, a TAMP system orchestrates a mobile manipulator (a robot arm on a mobile base) to fulfill a multi-item order. The high-level task plan might be: Navigate to Bin A, Pick Item X, Navigate to Bin B, Pick Item Y, Navigate to Packing Station, Place Items. The motion planner must solve for:

• Feasible navigation paths around shelves, other robots, and human workers.
• Precise arm trajectories to grasp items of varying shapes from cluttered bins, often requiring regrasp planning.
• Integrated sequences where navigation and manipulation motions are interleaved and timed to avoid collisions with the environment and the robot's own body.

A domestic robot instructed to "make a cup of coffee" must decompose this into a symbolic action sequence: Open cabinet, Grasp mug, Place mug on counter, Open fridge, Grasp milk, Pour milk, .... Each symbolic action has geometric constraints:

• Open cabinet requires a motion plan to reach the handle and pull along a constrained arc.
• Grasp mug requires 6D pose estimation and a force-closure grasp that avoids tipping.
• Pour milk necessitates a compliant motion where the robot senses contact and adjusts torque to avoid spillage, tightly coupling task logic with low-level force control.

Disassembling a discarded smartphone for recycling is a classic TAMP challenge due to uncertainty and complex physical interactions. The system must:

• Perceive and localize screws, clips, and connectors using vision.
• Sequence tools: Plan to use a screwdriver bit, then a suction gripper, then a prying tool.
• Handle uncertainty: If a screw is stripped, the planner must replan at the task level (e.g., switch to a destructive prying method) and generate new motions. This requires conditional planning where geometric feasibility checks inform high-level decision trees, making the system robust to real-world variability.

In robot-assisted surgery, TAMP frameworks can automate sub-tasks like suture tying or tool hand-off. For a suturing task:

• The task planner breaks it down: Grasp needle, Pierce tissue at point A, Reposition, Pierce at point B, Pull thread, Tie knot.
• The motion planner must generate:
  • Millimeter-precise, tremor-free trajectories constrained by the patient's anatomy (modeled as a collision map).
  • Compliant motions that account for tissue deformation using force feedback.
  • Dual-arm coordination for bimanual knot-tying. The tight integration ensures each high-level step is physically executable within safety-critical bounds.

Assembling an engine block involves inserting pistons, connecting rods, and bolts—a problem of compliant assembly. A TAMP system handles this by:

• Generating a symbolic assembly sequence respecting mechanical constraints (e.g., piston must be inserted before connecting rod is attached).
• **Planning fine motion strategies for each insertion, such as spiral search or force-guided alignment, which are triggered by the task planner when a "insert peg-in-hole" action is selected.
• Monitoring execution: If a force/torque sensor detects a jam, the task planner may decide to retract, re-align, and retry, generating new motion parameters for each attempt. This closed-loop between discrete decisions and continuous control is the hallmark of TAMP.

TAMP is implemented using specialized algorithms that bridge the symbolic-geometric divide:

• PDDLStream: Extends the Planning Domain Definition Language (PDDL) with sampling procedures for continuous parameters (like grasp poses or paths). The planner interleaves symbolic search with calls to a motion planner to prove feasibility.
• Logic-Geometric Programming (LGP): Formulates the problem as a mathematical program with discrete logical variables and continuous geometric constraints, solved via combined optimization.
• Hierarchical Planning in Belief Space: For problems with perception uncertainty, this plans over belief states (distributions over world states), where high-level actions have associated perception and manipulation policies to reduce uncertainty.
• Integrated Task and Motion Planning (ITAMP): An approach that performs a single search over a hybrid space of discrete actions and continuous parameters, avoiding the separation between task and motion layers.

The high-level reasoning component of TAMP that operates on an abstract, symbolic representation of the world. It determines the logical sequence of actions (e.g., 'pick up block A', 'place on table') required to achieve a goal, ignoring geometric feasibility.

• Uses Planning Domain Definition Language (PDDL) to model actions, preconditions, and effects.
• Solves a discrete search problem, often with algorithms like Graphplan or Fast Forward (FF).
• Outputs a plan skeleton, which is then validated and fleshed out by the motion planner.

The low-level geometric component of TAMP that computes a continuous, collision-free path for the robot's joints or end-effector through a configuration space. It answers 'how' to move, given a start and goal pose.

• Key algorithms include Probabilistic Roadmaps (PRM) and Rapidly-exploring Random Trees (RRT).
• Must satisfy kinematic constraints, avoid obstacles, and often optimize for path length or smoothness.
• In TAMP, motion planning is invoked repeatedly to check the feasibility of each symbolic action in the candidate plan.

The core TAMP methodology that interleaves symbolic and geometric planning to find a plan that is both logically correct and physically executable. It avoids the computational infeasibility of planning all symbols first, then all motions.

• Common architectures include hierarchical planning and interleaved sampling.
• Algorithms like Logic-Geometric Programming (LGP) and Perturbation-based TAMP search over hybrid spaces.
• Must handle the interdependence of actions; a feasible grasp for an object depends on where it was previously placed.

The specialized geometric and physical reasoning required to determine stable contact points and gripper orientations for picking up an object. It is a critical sub-problem within the 'pick' action of a TAMP sequence.

• Evaluates candidate grasps based on force closure, stability metrics, and reachability.
• Often uses pre-computed grasp databases or sampling-based algorithms like GraspIt!.
• In TAMP, grasp planning is tightly coupled with motion planning to ensure the chosen grasp is kinematically feasible from the robot's current configuration.

The continuous geometric checking required throughout a TAMP solution to ensure the robot, manipulated objects, and environment do not intersect. It is a fundamental constraint for motion feasibility.

• Uses efficient bounding volume hierarchies (BVH) and signed distance fields (SDF) for real-time computation.
• Dynamic obstacles (like other moving robots or humans) require predictive models and reactive replanning.
• TAMP must reason about collisions for the entire plan duration, including objects being carried, which change the robot's collision geometry.

An advanced, real-time control strategy often used to execute the trajectories generated by a TAMP system. MPC handles model inaccuracies and small disturbances during physical operation.

• Solves a finite-horizon optimal control problem online, using a dynamic model of the robot.
• Can incorporate force feedback for compliant contact, crucial for tasks like insertion or assembly.
• Acts as the final layer that translates the TAMP plan's intended motions into precise, reactive joint torques and velocities.