Plan For Physics

What Plan For Physics Actually Is

It's a Python library for generating physically valid trajectories and motion plans using constraint-based optimization. You define a scene with objects, masses, joints, and environmental constraints, then it spits out trajectories that won't violate Newtonian physics. That's the short version. The longer version is that it's built on top of CasADi and IPOPT, which means it's fast if you know what you're doing and a pain to debug if you don't. I first ran into this tool when a colleague suggested we use it for a robotics arm path-planning problem. We'd been writing custom dynamics solvers by hand, which worked until the robot started interacting with objects of varying mass and friction. Plan For Physics handled the dynamics internally so we didn't have to derive the Lagrangian equations ourselves.

Plan For Physics Setup and Basics

Installation is straightforward if you have Python 3.9 or later and pip available: pip install plan-for-physics It depends on CasADi, numpy, scipy, and sometimes meshio if you're working with 3D geometries. If you're on Windows and hit DLL errors with IPOPT, you'll need to compile the optimizer yourself or use the conda forge version. Linux users rarely have this problem. Once installed, the basic workflow looks like this: from plan_for_physics import Scene, RigidBody, ConstraintSolver scene = Scene() box = RigidBody("box", mass=2.5, shape="cube", dimensions=[0.1, 0.1, 0.1]) scene.add(box) solver = ConstraintSolver(scene) solution = solver.solve() That's the skeleton. In practice you're going to add joints, apply forces, set contact constraints, and define goal states. The API is reasonably clean but the documentation assumes you already understand the underlying optimization formulation, which most people don't.

The hard part isn't installing it. It's setting up the constraints correctly.

How It Actually Works Under the Hood

Plan For Physics formulates your physics problem as a nonlinear programming (NLP) problem. Time gets discretized into nodes. Your state variables—position, velocity, orientation, angular velocity—are defined at each node. The solver then finds values for all those variables that satisfy the equations of motion plus any additional constraints you specified. This is fundamentally different from a forward physics simulator. A simulator takes initial conditions and integrates forward. Plan For Physics treats the entire trajectory as unknowns and solves for everything simultaneously. The advantage is that it can plan around obstacles, respect force limits, and hit target states. The disadvantage is that NLP problems scale poorly. A trajectory with 100 time nodes and 10 state variables per node is already a medium-sized problem. Add more bodies and things get slow. I learned this the hard way when I tried to plan a dual-arm robotic system with contact-rich interactions. The NLP had roughly 5,000 variables and 3,000 constraints. First run took about four hours and failed to converge. Second attempt I reduced the time discretization from 200 nodes to 80 and added warm-start values from a coarser solution. Converged in about twelve minutes. That's the pattern you'll repeat: solve coarse, refine, repeat.

Common Use Cases

Motion planning for robotic manipulators is the biggest one. You define the robot kinematics, the payload, the environment obstacles, and the target grasp configuration. Plan For Physics finds a trajectory that moves from start to finish while respecting dynamics and avoiding collisions. Another common use is animation and simulation for game development or film. You can specify keyframe-like goal states and let the optimizer fill in physically plausible intermediate motion. This is particularly useful for characters interacting with physics-based props. There's also the pedagogical angle. If you're teaching classical mechanics and want students to see how changing a parameter affects a trajectory, this tool lets them do that without writing integration code. Students often struggle with the constraint setup at first, but once they get it, it's genuinely powerful.

Things the Documentation Won't Tell You

Constraint initialization matters more than anyone admits. If you provide poor initial guesses for the solver, it may converge to a locally optimal but physically unrealistic trajectory. Or it might not converge at all. I spent two days debugging a solution where the planner kept producing trajectories that passed through solid objects. The issue wasn't the collision constraints being wrong. It was that my initial guess for the position variables was too far from any feasible solution. Once I seeded the optimizer with a linear interpolation between start and goal states, convergence became reliable. Contact modeling is another area where expectations and reality diverge. Plan For Physics supports contact constraints, but modeling frictional contact correctly requires careful tuning of penalty parameters. The default settings work for simple cases. For anything involving sliding, sticking, or repeated impacts, you'll likely need to adjust the regularization parameters. There's no universal recipe. You experiment until it stops producing garbage. Another pitfall: the solver treats everything as a continuous optimization problem. That means if your problem has discrete decisions—like whether a robot should grab an object or push it—the tool won't handle that natively. You'd need to formulate it as a mixed-integer problem, which means leaving the Plan For Physics ecosystem and using something like CasADi directly with an MILP solver. I ran into this when trying to plan a pick-and-place sequence where the grasp choice depended on object orientation. Split it into two separate planning passes and merged the results manually. Took longer than I'd like to admit.

Performance and Scaling

For small problems—one rigid body, simple constraints—solving typically takes between one and five seconds on a modern laptop. Medium problems, like a six-degree-of-freedom arm with obstacle avoidance, run anywhere from thirty seconds to three minutes depending on constraint complexity. Large problems with multiple bodies and complex contacts can take ten minutes or more, and convergence is never guaranteed. If you're working in a production environment where response time matters, you'll want to look into warm-starting the solver with solutions from similar previous problems. Plan For Physics supports this through its solver options. I typically save the last successful state and use it as the initial guess for the next query. This cuts solution time by roughly sixty percent in my experience. Memory usage is another consideration. Each additional time node increases memory linearly, but the constraint matrix sparsity pattern can become expensive to store for complex contact scenarios. On a machine with 16 GB of RAM, I've successfully solved problems with around 5,000 variables. Problems beyond that start swapping and becoming unusably slow.

A Real Edge Case I Hit

I was working on a project involving a pendulum that needed to swing up and catch a ball at the apex of its arc. The ball was falling under gravity, and the timing had to be precise. Plan For Physics handled the pendulum dynamics fine. The issue was that the ball's trajectory wasn't part of the optimization variables—it was a predefined external input. The planner found a solution, but when I simulated it, the pendulum missed the ball by several centimeters. The root cause was numerical. The solver was optimizing the pendulum trajectory with a time step of 0.01 seconds. The ball's position at the catch moment was computed from an analytical formula, not from the same discretization. The mismatch between the solver's time grid and the analytical evaluation caused the error. The workaround was to discretize the ball's trajectory as well and include it as part of the optimization, even though its dynamics were simple. That aligned the time grids and eliminated the miss. It added maybe twenty variables to the problem, which was negligible compared to the time I'd already lost debugging it.

Alternatives Worth Knowing About

If Plan For Physics doesn't fit your needs, there are other options. PyDy is more focused on symbolic dynamics derivation and forward simulation. It's better if you need to understand the equations rather than just solve them. MuJoCo is excellent for contact-rich simulation and real-time applications but is primarily a simulator, not a planner. Isaac Sim from NVIDIA handles large-scale physics planning with GPU acceleration but requires a significant compute setup. For pure trajectory optimization, CasADi with its IRK or Gauss-Legendre collocation methods gives you more control but also more work. Plan For Physics sits somewhere in between: more accessible than raw CasADi, more planning-focused than MuJoCo. Whether that's the right spot for you depends on your specific problem.

Bottom Line

Plan For Physics is a solid tool for trajectory and motion planning when your problem fits within its constraint-based optimization framework. It handles dynamics correctly, it's reasonably fast for small to medium problems, and the Python API is clean enough that you can prototype quickly. But it will trip you up on constraint initialization, contact tuning, and problems that mix continuous and discrete decisions. The documentation is adequate but not comprehensive, and you'll spend more time reading source code and experimenting than following tutorials. If you're comfortable with optimization concepts and willing to debug when things don't converge, it's worth learning. If you need something that just works out of the box for complex real-world scenarios, you might find yourself frustrated and looking elsewhere.