Planning for Reality: Robots Learn to Move with Physics

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Author: Denis Avetisyan

A new approach combines physics simulation and advanced optimization to enable robots to generate feasible plans that account for real-world dynamics and contact forces.

The framework defines robotic action through symbolic parameters-such as designating locations like ‘Table1’ or ‘Exit’-allowing a single parameterized action like $moveTo(Table1, …)$ to yield diverse motions, and further optimizes these plans via parallel simulations and cross-entropy methods to navigate the inherent variability of physical systems.
The framework defines robotic action through symbolic parameters-such as designating locations like ‘Table1’ or ‘Exit’-allowing a single parameterized action like $moveTo(Table1, …)$ to yield diverse motions, and further optimizes these plans via parallel simulations and cross-entropy methods to navigate the inherent variability of physical systems.

This work presents a cross-entropy optimization method for task and motion planning that implicitly incorporates physics and controller limitations within a simulated environment.

While robot autonomy demands seamless integration of high-level task planning with low-level motion control, existing methods often sacrifice physical realism for computational tractability. This limitation hinders reliable performance when complex manipulation and contact dynamics are involved; in ‘Cross-Entropy Optimization of Physically Grounded Task and Motion Plans’, we address this challenge by leveraging GPU-parallelized physics simulation and cross-entropy optimization to directly learn feasible robot plans. Our approach samples controller parameters within a physics engine, enabling the discovery of solutions that account for dynamics, contacts, and real-world controller limitations-allowing for direct execution on the physical robot. Could this method unlock more robust and adaptable robot behavior in unstructured environments?

The Inevitable Complexity of Robotic Coordination

Robotic systems frequently encounter difficulties when tasked with activities demanding the simultaneous and precise coordination of movement and object interaction. This challenge stems from the inherent complexity of integrating motion planning – charting a path through space – with manipulation planning, which focuses on how to physically interact with an object. Unlike simpler tasks, intricate coordination requires anticipating how each movement affects the next, and how manipulation alters the robot’s own stability and reach. Consider a scenario where a robot must assemble a complex structure; it cannot simply reach for parts without accounting for the shifting center of gravity or potential collisions with surrounding objects. This interplay between locomotion and dexterity pushes the limits of current robotic control algorithms, demanding solutions that can effectively manage a high-dimensional state space and respond to unforeseen disturbances in real-time.

Conventional robotic planning algorithms, while theoretically sound, encounter significant hurdles when applied to real-world scenarios due to computational demands. As the intricacy of a task – involving more movements, objects, or constraints – increases, the time required for these algorithms to generate a viable plan grows exponentially. This phenomenon, often described as “combinatorial explosion,” renders many sophisticated planning techniques impractical for timely execution. For example, finding a collision-free path for a robotic arm manipulating an object amidst obstacles can quickly become intractable, even for moderately complex environments. Consequently, robots are often limited to simplified tasks or pre-programmed routines, hindering their adaptability and widespread use in dynamic, unstructured settings. Researchers are actively exploring methods – such as sampling-based planning, hierarchical planning, and machine learning – to mitigate these computational costs and enable more efficient, real-time robotic manipulation.

Effective interaction with the physical world demands more than just moving a robotic arm; it necessitates a seamless integration of task and motion planning, particularly in dynamic and cluttered spaces. This involves not simply charting a path to an object, but intelligently coordinating the robot’s movements with the required manipulations – grasping, assembling, or rearranging – all while avoiding collisions and respecting physical constraints. Current research focuses on developing algorithms that can efficiently search the vast space of possible motions and tasks, enabling robots to respond to unforeseen obstacles and adapt to changing circumstances. The goal is to move beyond pre-programmed sequences and create systems capable of real-time, robust performance, mirroring the dexterity and adaptability humans exhibit when navigating and manipulating objects in complex environments.

Mobile manipulation becomes significantly more challenging when robots encounter commonplace obstacles during task execution. Simple environments allow for straightforward path planning, but the introduction of box-shaped or ramp-shaped obstructions dramatically increases computational demands. These obstacles necessitate not only adjustments to the robot’s trajectory to avoid collisions, but also alterations to its manipulation strategy; a robot might need to re-orient its end-effector, adjust its grip, or even temporarily reposition itself to successfully interact with objects. The combination of mobile base movement and arm manipulation, coupled with obstacle avoidance, creates a high-dimensional planning problem that quickly exceeds the capabilities of traditional algorithms, requiring more sophisticated approaches to achieve robust and efficient performance in realistic, cluttered scenarios.

This mobile manipulator efficiently solves manipulation tasks like pick-and-place and block-pushing by leveraging environmental features such as slopes to optimize movement.
This mobile manipulator efficiently solves manipulation tasks like pick-and-place and block-pushing by leveraging environmental features such as slopes to optimize movement.

Formalizing Intent: Symbolic Representation and Planning

Planning Domain Definition Language (PDDL) is utilized to formally represent robotic tasks by defining actions and their associated requirements. Each action is described by its name, parameters, preconditions – the states that must be true for the action to be executable – and effects, which detail how the action changes the environment. These preconditions and effects are expressed as logical predicates, allowing the planning system to reason about the feasibility of action sequences. By defining tasks in this symbolic manner, the system can explore different action combinations to achieve a desired goal state, independent of the specific robot or environment details, enabling a level of abstraction and reusability.

A Symbolic Plan, generated from the symbolic representation of a task, functions as a high-level sequence of actions designed to achieve a defined goal. This plan details what needs to be accomplished, specifying the order of operations without immediately addressing how those operations are physically executed. The plan utilizes preconditions and effects defined within the PDDL language to logically connect actions, ensuring that each step is only initiated when its necessary conditions are met and that the resulting state allows for subsequent actions. This abstraction enables task decomposition and strategic reasoning prior to engaging with the complexities of physical implementation and allows for exploration of multiple potential solutions before committing to a specific execution pathway.

Cross-Entropy Optimization (CEO) is employed as a stochastic search algorithm to identify parameters for the symbolic plan that maximize the probability of successful physical execution. CEO operates by iteratively sampling candidate solutions from a probability distribution, evaluating their performance within a physics simulator, and then updating the distribution to favor solutions with higher observed rewards. This process involves estimating the parameters of the distribution – typically a Gaussian distribution defined by a mean $\mu$ and standard deviation $\sigma$ – based on the elite samples from each iteration. The algorithm refines the plan parameters by narrowing the distribution around these successful solutions, effectively concentrating the search on promising areas of the solution space and allowing for the discovery of low-cost plans that satisfy the symbolic representation.

The evaluation of potential plans relies on a physics simulator which determines the feasibility of action sequences. Initial testing of a pick and place task, incorporating a ramp-shaped obstacle, yielded a success rate of approximately 0.1%. This low initial success rate indicated significant challenges in translating symbolic plans into effective physical actions. However, through iterative application of Cross-Entropy Optimization – a process of repeatedly simulating plans, evaluating their performance in the physics simulator, and adjusting parameters to favor successful outcomes – the system’s performance was improved. This iterative approach allows for the refinement of plans based on simulated physical interactions, ultimately increasing the likelihood of successful task completion.

The demonstrated robotic policy successfully executed both pick-and-place maneuvers around a ramp-shaped obstacle and more complex move-and-push tasks using standard low-level controllers, as shown in the included video.
The demonstrated robotic policy successfully executed both pick-and-place maneuvers around a ramp-shaped obstacle and more complex move-and-push tasks using standard low-level controllers, as shown in the included video.

From Abstraction to Action: Whole-Body Coordination

Plan Realization is the process of translating a high-level, symbolic plan into concrete robot actions. This involves determining specific parameters – such as joint angles, velocities, and forces – for each degree of freedom to execute the plan. A Cost Function is central to this process; it quantitatively evaluates the quality of different possible motions and parameter sets. This function assigns a numerical value based on factors like execution time, energy consumption, and proximity to obstacles, allowing the system to select the optimal solution from a range of feasible options. The Cost Function guides the search for the best realization of the symbolic plan, effectively bridging the gap between abstract goals and physical execution.

The Cost Function used in plan realization incorporates a Feasibility term to guarantee physically possible robot motions. This term evaluates proposed trajectories based on kinematic and dynamic constraints, such as joint limits, velocity limits, and acceleration limits. Specifically, the Feasibility component penalizes plans that violate these limits, effectively driving the optimization process towards solutions that the robot can physically execute. The magnitude of the penalty is often weighted to prioritize Feasibility alongside other plan qualities, such as execution time or energy consumption. This ensures that while the plan aims to be optimal, it remains within the robot’s physical capabilities, preventing collisions or damaging movements.

Whole-Body Control (WBC) represents a control paradigm that simultaneously manages the motion of a robot’s base, arms, and other appendages as a unified system. This differs from traditional control schemes that often address each joint or limb independently. By coordinating the entire body, WBC allows robots to satisfy complex kinematic and dynamic constraints imposed by the environment and the task at hand. This capability is essential for tasks requiring precise manipulation while maintaining balance, navigating cluttered spaces, or interacting with objects in a physically grounded manner. The approach utilizes optimization-based methods to compute joint torques and velocities that achieve desired end-effector positions and orientations while respecting joint limits, collision avoidance, and balance requirements, effectively enabling the robot to respond to external disturbances and maintain stability during dynamic maneuvers.

Geometric Fabrics represent a computationally efficient approach to whole-body control by formulating the robot’s inverse kinematics as a geometric problem rather than relying on iterative optimization. This method pre-computes and stores possible robot configurations, effectively creating a “fabric” of feasible solutions. During execution, the desired motions are mapped onto this fabric, allowing for rapid retrieval of joint angles without solving complex equations in real-time. This pre-computation significantly reduces the computational burden, enabling the robot to react quickly to changing environments and maintain stable control, particularly crucial for dynamic tasks and applications demanding low latency.

Simulation results demonstrate the robot leverages a ramp to slide a cube past an obstacle, a strategy it does not employ when facing a box, and successfully implements a move-and-push approach in varied scenarios.
Simulation results demonstrate the robot leverages a ramp to slide a cube past an obstacle, a strategy it does not employ when facing a box, and successfully implements a move-and-push approach in varied scenarios.

Toward Adaptive Systems: Robustness and Future Directions

Robotic manipulation often struggles with tasks demanding intricate coordination and adaptability, but a new approach integrates three core principles to overcome these challenges. Symbolic planning provides the high-level reasoning needed to define task goals and sequences, while optimization refines these plans to account for real-world constraints and uncertainties. Crucially, this is coupled with whole-body control, allowing the robot to coordinate movements across its entire structure-arms, torso, and base-to maintain stability and precision during complex actions. This synergistic combination moves beyond pre-programmed routines, enabling robots to dynamically adjust to changing circumstances and successfully execute tasks requiring nuanced interaction with the environment, ultimately paving the way for more versatile and capable robotic systems.

A core component of enabling complex robotic manipulation lies in the synergy between physics simulation and algorithmic efficiency. The system leverages a physics simulator to rapidly prototype and refine control strategies, predicting the outcome of actions before they are executed on a physical robot. This predictive capability is bolstered by algorithms like Geometric Fabrics, which facilitate swift computation of collision-free paths and stable grasps. The combination allows for real-time performance – critical for dynamic environments – and inherent adaptability, as the robot can replan in response to unexpected disturbances or changes in its surroundings. This approach moves beyond pre-programmed sequences, granting the robot the capacity to react and adjust, ultimately leading to more robust and reliable manipulation capabilities.

The developed robotic framework exhibits a noteworthy capacity for navigating complex environments and interacting with objects despite the presence of obstacles. Through the integration of path planning algorithms, specifically the A* algorithm, and real-time physics simulation, the system can efficiently compute trajectories that avoid collisions with structures like boxes or ramps. This robust navigation isn’t merely about avoiding obstacles, but also enabling continued task execution around them. Demonstrated through pick-and-place and move-and-push tasks, the robot maintains functionality even when faced with physical impediments, showcasing its adaptability and potential for use in unstructured, real-world scenarios where predictable environments are not guaranteed.

Efficient navigation around obstacles is achieved through the implementation of the A* path planning algorithm, guiding the mobile manipulator during complex tasks. Testing revealed a slight performance difference between simulation and real-world execution; a pick and place maneuver took 35 seconds in the physical environment compared to 21 seconds in simulation, while a move and push task required 38 seconds as opposed to the simulated 21. This discrepancy is attributed to inherent limitations in actuator responsiveness and the effects of friction. To optimize computational efficiency, the algorithm employed a decreasing sampling rate; initial iterations utilized a rate of 3000, which linearly decreased to 300 as the optimization process progressed, allowing for faster convergence without sacrificing accuracy in path planning.

Cross-entropy optimization successfully identified viable mobile base and end-effector trajectories (cyan) amidst a field of failed attempts (orange), guided by parameter values indicated by cross markers and evaluated within a simulated environment including obstacles and padding.
Cross-entropy optimization successfully identified viable mobile base and end-effector trajectories (cyan) amidst a field of failed attempts (orange), guided by parameter values indicated by cross markers and evaluated within a simulated environment including obstacles and padding.

The pursuit of robust robotic systems, as detailed in this work concerning task and motion planning, inherently acknowledges the transient nature of stability. While the paper focuses on achieving feasible plans through cross-entropy optimization and physics simulation, it implicitly recognizes that any realized controller will eventually succumb to the inevitable effects of real-world variability. As Donald Knuth observed, “Premature optimization is the root of all evil.” This resonates with the approach presented; the method prioritizes finding viable plans, acknowledging that perfect, perpetually stable control is an asymptotic goal. The optimization process navigates the inherent complexities of contact dynamics, accepting that latency – the ‘tax every request must pay’ – is a constant factor in physical systems. The work doesn’t eliminate these challenges, but instead addresses them within a framework that anticipates graceful degradation rather than striving for unattainable perfection.

What’s Next?

The presented work, while demonstrating a pathway toward more robust task and motion planning, merely postpones the inevitable entropy. Every successful plan is a temporary reprieve, a localized decrease in disorder before the system-robot, environment, task-reverts to a higher state of uncertainty. The reliance on physics simulation, while advantageous, introduces a fidelity gap – a persistent lag between the modeled world and its messy, unpredictable counterpart. Bridging this gap isn’t about increasing simulation accuracy, but accepting that perfect fidelity is an asymptotic limit, never truly reached.

Future investigations will inevitably confront the question of plan adaptation. A plan, once viable, is a historical artifact. The challenge isn’t creating plans that never fail, but building systems capable of gracefully absorbing failure, of re-optimizing in real-time against the current of unforeseen circumstances. This necessitates a move beyond cross-entropy as a purely optimization tool, and toward its use as a mechanism for evolution – allowing plans to mutate and adapt in response to the pressures of their environment.

Ultimately, the true metric isn’t plan success rate, but the system’s capacity to endure. Technical debt, in this context, isn’t just computational cost; it’s the accumulated compromises necessary to achieve any progress. Each simplification, each approximation, represents a future moment of truth. The question isn’t whether the system will fail, but how it will age.

Original article: https://arxiv.org/pdf/2512.11571.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-12-16 07:15