Collision Detection

Efficient collision detection systems universally employ a two-phase architecture to balance performance and accuracy.

• Broad Phase: This initial, low-fidelity pass quickly identifies pairs of objects that could be colliding. It uses spatial data structures like Bounding Volume Hierarchies (BVH), Spatial Hashing, or Sweep and Prune to cull obviously non-intersecting objects, drastically reducing the number of pairs sent for expensive precise checks.
• Narrow Phase: For each candidate pair from the broad phase, this phase performs exact geometric intersection tests. Algorithms like the Gilbert–Johnson–Keerthi (GJK) algorithm for convex shapes or the Separating Axis Theorem (SAT) determine precise contact points, penetration depths, and surface normals, which are critical for the subsequent contact dynamics resolution.

A Bounding Volume Hierarchy (BVH) is a tree structure used to organize objects in space for efficient broad-phase culling. Each node in the tree has a simple bounding volume—like an Axis-Aligned Bounding Box (AABB) or a sphere—that encloses all the geometry of its children.

• Construction: The tree is built by recursively partitioning a set of objects, creating a hierarchy where parent volumes fully contain their children.
• Traversal: During collision queries, the tree is traversed; if the bounding volumes of two nodes do not overlap, all their children are guaranteed not to collide and are culled without further tests.
• Dynamic Updates: For moving objects, refitting algorithms update the bounding volumes up the tree, which is faster than rebuilding the entire hierarchy each frame. BVHs are foundational in engines like NVIDIA Isaac Sim and MuJoCo.

The GJK algorithm is a highly efficient iterative method for computing the distance between two convex shapes and detecting collision. It is the standard narrow-phase algorithm in modern physics engines like Bullet and ODE.

• Core Mechanism: GJK uses the concept of a Minkowski Difference. If two convex sets A and B intersect, the Minkowski difference (A - B) contains the origin. The algorithm iteratively constructs a simplex (a point, line segment, triangle, or tetrahedron) within this difference to check for origin containment.
• Output: It returns a boolean collision result. A companion algorithm, the Expanding Polytope Algorithm (EPA), can be used after GJK detects a collision to compute the penetration depth and contact normal.
• Efficiency: Its speed comes from using support functions, which return the farthest point on a shape in a given direction, making it ideal for complex convex meshes.

Continuous Collision Detection (CCD), also known as time-of-impact detection, is essential for preventing tunneling—where fast-moving or thin objects pass through each other between discrete simulation time steps.

• The Problem: Standard discrete collision detection only checks for intersections at the end of each time stepping interval. A bullet moving faster than the thickness of a wall can be on one side at time t and the other side at time t+Δt, never registering a collision.
• The Solution: CCD models the continuous motion of objects between time steps (often as a linear sweep). It computes the exact time of impact, allowing the physics engine to roll back the simulation to that moment for accurate contact dynamics resolution.
• Use Case: Critical for simulating fast projectiles, precise robotic grasping, and any simulation requiring high simulation fidelity with large time steps or high velocities.

After collision is detected, the system must generate a contact manifold—a simplified representation of the intersecting surfaces—for the constraint-based solver to resolve physically.

• Contact Point: The precise 3D location where objects touch.
• Contact Normal: A unit vector perpendicular to the collision surface at the contact point, defining the direction of the separation impulse.
• Penetration Depth: The distance one object has intersected another, used to calculate the magnitude of the corrective force.
• Persistent Contact: For objects resting or sliding, engines like MuJoCo use warm starting, caching contact information from the previous time step to improve solver stability and performance. The manifold data is the primary input for solving the Linear Complementarity Problem (LCP) that models friction and restitution.

Collision detection is not only for dynamics but also for simulating robotic sensors that perceive contact and proximity.

• Ray Casting: A fundamental technique for simulating LiDAR, proximity sensors, and touch. A virtual ray is projected from a sensor origin. The collision detection system computes the first intersection with any object in the scene, returning the hit point, distance, and surface normal. This is a specialized, single-ray form of collision query.
• Contact Sensor: A virtual sensor attached to a robot link that triggers a boolean signal or reports contact forces when the link's geometry intersects with another object. This is crucial for simulating tactile feedback or bump sensors.
• Volume Queries: Simulating sensors like ultrasonic range finders may involve casting a volume (e.g., a cone) and detecting all collisions within it. These queries rely on the same underlying broad-phase and narrow-phase infrastructure as dynamics collision.

A physics engine is the core software library responsible for simulating Newtonian mechanics in a virtual environment. It integrates several key subsystems:

• Rigid-body dynamics to calculate object motion from forces.
• Collision detection to identify intersections.
• Contact dynamics solvers to compute collision responses (forces, friction). Engines like MuJoCo, Bullet, and ODE differ in their numerical methods (e.g., penalty-based vs. constraint-based solvers) which trade off between speed, stability, and physical accuracy.

Contact dynamics refers to the mathematical modeling and computational resolution of forces generated when simulated objects collide or maintain persistent contact. After collision detection identifies an intersection, the contact dynamics solver calculates the appropriate response to prevent inter-penetration and model physical effects:

• Normal force using a restitution coefficient (bounciness).
• Tangential friction force using static and dynamic friction coefficients.
• Resting contacts for stable stacking. Solvers often frame this as a Linear Complementarity Problem (LCP) or use a faster, less accurate penalty-based method.

A constraint-based solver is the algorithmic core in advanced physics engines that calculates forces to satisfy hard kinematic and dynamic limits. It treats contact non-penetration and joint limits as mathematical constraints that must not be violated. The primary computational challenge is solving a Linear Complementarity Problem (LCP) or a similar numerical optimization at each simulation time step to find the correct set of contact impulses. This method produces more stable and physically plausible results for complex, multi-contact scenarios (like a robot hand grasping an object) compared to simpler spring-damper penalty methods.

Collision detection is typically performed in two algorithmic phases for efficiency:

• Broad Phase: A fast, approximate culling stage that identifies pairs of objects that are potentially colliding. It uses spatial partitioning data structures like Bounding Volume Hierarchies (BVH), Sweep and Prune, or Grids to avoid expensive O(n²) pairwise checks.
• Narrow Phase: A precise geometric intersection test performed on the candidate pairs from the broad phase. This stage uses algorithms like the Gilbert–Johnson–Keerthi (GJK) algorithm for convex shapes or Minkowski Portal Refinement (MPR) to compute exact contact points, penetration depth, and separating axes.

Simulation fidelity measures how accurately a virtual environment replicates real-world physics and sensor outputs. High-fidelity collision detection is a critical contributor. Key aspects include:

• Geometric accuracy of collision meshes (convex decomposition vs. raw mesh).
• Temporal resolution of collision checks (sub-stepping).
• Physical correctness of material properties (friction, restitution). Low fidelity can lead to a significant reality gap, where policies trained in simulation fail on physical hardware because contact interactions are unrealistic.

A contact sensor is a simulated version of a physical touch or force-torque sensor. It is implemented by querying the collision detection and contact dynamics system. When a collision is detected on a specific robot link, the sensor can output:

• Binary contact state (touch/no-touch).
• Contact force vector and magnitude.
• Contact point location on the link's surface. These signals are essential for training and testing manipulation policies, allowing robots to sense grasps, slips, and collisions in simulation before real-world deployment.